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Journal articles on the topic 'Formule de trace de'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 March 2025

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1

Hillairet, Luc. "Formule de trace sur une surface euclidienne à singularités coniques." Comptes Rendus Mathematique 335, no. 12 (December 2002): 1047–52. http://dx.doi.org/10.1016/s1631-073x(02)02596-7.

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2

Mœglin, Colette, and J. L. Waldspurger. "La formule des traces locale tordue." Memoirs of the American Mathematical Society 251, no. 1198 (January 2018): 0. http://dx.doi.org/10.1090/memo/1198.

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3

Chattopadhyay, Arup, and Kalyan B. Sinha. "Koplienko Trace Formula." Integral Equations and Operator Theory 73, no. 4 (June 21, 2012): 573–87. http://dx.doi.org/10.1007/s00020-012-1978-4.

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4

Knightly, Andrew, and Charles Li. "A relative trace formula proof of the Petersson trace formula." Acta Arithmetica 122, no. 3 (2006): 297–313. http://dx.doi.org/10.4064/aa122-3-5.

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5

Ferrari, Axel. "Théorème de l’Indice et Formule des Traces." manuscripta mathematica 124, no. 3 (August 14, 2007): 363–90. http://dx.doi.org/10.1007/s00229-007-0130-2.

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6

Hillairet, Luc. "FORMULE DE TRACE SEMI-CLASSIQUE SUR UNE VARIETE DE DIMENSION 3 AVEC UN POTENTIEL DE DIRAC." Communications in Partial Differential Equations 27, no. 9-10 (January 12, 2002): 1751–91. http://dx.doi.org/10.1081/pde-120016127.

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7

Akiyama, Shigeki, and Yoshio Tanigawa. "The Selberg trace formula for modular correspondences." Nagoya Mathematical Journal 117 (March 1990): 93–123. http://dx.doi.org/10.1017/s0027763000001823.

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In Selberg [11], he introduced the trace formula and applied it to computations of traces of Hecke operators acting on the space of cusp forms of weight greater than or equal to two. But for the case of weight one, the similar method is not effective. It only gives us a certain expression of the dimension of the space of cusp forms by the residue of the Selberg type zeta function. Here the Selberg type zeta function appears in the contribution from the hyperbolic conjugacy classes when we write the trace formula with a certain kernel function ([3J, [4], [7], [8], [9], [12]).

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8

Chaudouard, Pierre-Henri, and Michał Zydor. "Le transfert singulier pour la formule des traces de Jacquet–Rallis." Compositio Mathematica 157, no. 2 (February 2021): 303–434. http://dx.doi.org/10.1112/s0010437x20007599.

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RésuméLa formule des traces relative de Jacquet–Rallis (pour les groupes unitaires ou les groupes linéaires généraux) est une identité entre des périodes des représentations automorphes et des distributions géométriques. Selon Jacquet et Rallis, une comparaison de ces deux formules des traces relatives devrait aboutir à une démonstration des conjectures de Gan–Gross–Prasad et Ichino–Ikeda pour les groupes unitaires. Les termes géométriques des groupes unitaires ou des groupes linéaires sont indexés par les points rationnels d'un espace quotient commun. Nous établissons que ces termes géométriques peuvent être vus comme des fonctionnelles sur des espaces d'intégrales orbitales semi-simples régulières locales. En outre, nous montrons que point par point ces distributions sont en fait égales, via l'identification des espaces d'intégrales orbitales locales donnée par le transfert et le lemme fondamental (essentiellement connus dans cette situation). Cela donne leur comparaison et cela clôt la partie géométrique du programme de Jacquet–Rallis. Notre résultat principal est donc un analogue de la stabilisation de la partie géométrique de la formule des traces due à Langlands, Kottwitz et Arthur.

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9

Okikiolu, Kate. "a related trace formula." Duke Mathematical Journal 79, no. 3 (September 1995): 687–722. http://dx.doi.org/10.1215/s0012-7094-95-07918-6.

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10

Arthur, James. "A local trace formula." Publications mathématiques de l'IHÉS 73, no. 1 (December 1991): 5–96. http://dx.doi.org/10.1007/bf02699256.

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11

CHATTOPADHYAY, ARUP, and KALYAN B. SINHA. "Third order trace formula." Proceedings - Mathematical Sciences 123, no. 4 (November 2013): 547–75. http://dx.doi.org/10.1007/s12044-013-0145-4.

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12

Peng, ZhiFeng. "Stable local trace formula." Science China Mathematics 57, no. 12 (September 27, 2014): 2509–18. http://dx.doi.org/10.1007/s11425-014-4899-7.

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13

Flicker, Yuval Z., and David A. Kazhdan. "A simple trace formula." Journal d'Analyse Mathématique 50, no. 1 (December 1988): 189–200. http://dx.doi.org/10.1007/bf02796122.

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14

Delgado, Julio, and Michael Ruzhansky. "The bounded approximation property of variable Lebesgue spaces and nuclearity." MATHEMATICA SCANDINAVICA 122, no. 2 (April 8, 2018): 299. http://dx.doi.org/10.7146/math.scand.a-102962.

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In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on $\mathbb{R}^n$ in terms of global symbols.

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15

Peng, Zhifeng. "Multiplicity Formula and Stable Trace Formula." American Journal of Mathematics 141, no. 4 (2019): 1037–85. http://dx.doi.org/10.1353/ajm.2019.0027.

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16

Zydor, Michał. "LA VARIANTE INFINITÉSIMALE DE LA FORMULE DES TRACES DE JACQUET-RALLIS POUR LES GROUPES LINÉAIRES." Journal of the Institute of Mathematics of Jussieu 17, no. 4 (April 19, 2016): 735–83. http://dx.doi.org/10.1017/s1474748016000141.

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We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated à la Arthur multiplied by the absolute value of the determinant to the power $s\in \mathbb{C}$. It has a geometric side which is a sum of distributions $I_{\mathfrak{o}}(s,\cdot )$ indexed by the invariants of the adjoint action of $\text{GL}_{n}(\text{F})$ on $\mathfrak{gl}_{n+1}(\text{F})$ as well as a «spectral side» consisting of the Fourier transforms of the aforementioned distributions. We prove that the distributions $I_{\mathfrak{o}}(s,\cdot )$ are invariant and depend only on the choice of the Haar measure on $\text{GL}_{n}(\mathbb{A})$. For regular semi-simple classes $\mathfrak{o}$, $I_{\mathfrak{o}}(s,\cdot )$ is a relative orbital integral of Jacquet-Rallis. For classes $\mathfrak{o}$ called relatively regular semi-simple, we express $I_{\mathfrak{o}}(s,\cdot )$ in terms of relative orbital integrals regularised by means of zeta functions.

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17

Yang, Chuan-Fu. "Trace Formula on Transmission Eigenvalues of the Sturm–Liouville Problem." Zeitschrift für Naturforschung A 67, no. 8-9 (September 1, 2012): 429–34. http://dx.doi.org/10.5560/zna.2012-0041.

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In this paper, we consider eigenvalues and traces of a special Sturm-Liouville problem, which originates from an acoustic scattering problem with a spherically symmetric speed of sound. Regularized trace formulae on transmission eigenvalues of the Sturm-Liouville problem are obtained.

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18

GESZTESY, F., H. HOLDEN, B. SIMON, and Z. ZHAO. "HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS." Reviews in Mathematical Physics 07, no. 06 (August 1995): 893–922. http://dx.doi.org/10.1142/s0129055x95000347.

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We extend the trace formula recently proven for general one-dimensional Schrödinger operators which obtains the potential V(x) from a function ξ(x, λ) by deriving trace relations computing moments of ξ(λ, x) dλ in terms of polynomials in the derivatives of V at x. We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of ξ associated with boundary conditions other than the Dirichlet boundary condition underlying ξ.

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19

Levy, Jason. "A Note on the Relative Trace Formula." Canadian Mathematical Bulletin 38, no. 4 (December 1, 1995): 450–61. http://dx.doi.org/10.4153/cmb-1995-066-x.

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AbstractThis paper deals with the relative trace formula in the case of base change. Two truncations of the kernel are introduced, both based on the ideas of Arthur, and their integrals are shown to be asymptotic to each other. We also consider products of the kernel with automorphic forms, as these appear when comparing trace formulae (see [5]).

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20

Chaudouard, Pierre-Henri. "La formule des traces pour les algèbres de Lie." Mathematische Annalen 322, no. 2 (February 2002): 347–82. http://dx.doi.org/10.1007/s002080100274.

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21

Paris, Luis, and Loïc Rabenda. "Virtual and arrow Temperley–Lieb algebras, Markov traces, and virtual link invariants." Journal of Knot Theory and Its Ramifications 30, no. 06 (May 2021): 2150041. http://dx.doi.org/10.1142/s0218216521500413.

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Let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and standard polynomials in the variables [Formula: see text] For [Formula: see text] we denote by [Formula: see text] the virtual braid group on [Formula: see text] strands. We define two towers of algebras [Formula: see text] and [Formula: see text] in terms of diagrams. For each [Formula: see text] we determine presentations for both, [Formula: see text] and [Formula: see text]. We determine sequences of homomorphisms [Formula: see text] and [Formula: see text], we determine Markov traces [Formula: see text] and [Formula: see text], and we show that the invariants for virtual links obtained from these Markov traces are the [Formula: see text]-polynomial for the first trace and the arrow polynomial for the second trace. We show that, for each [Formula: see text] the standard Temperley–Lieb algebra [Formula: see text] embeds into both, [Formula: see text] and [Formula: see text], and that the restrictions to [Formula: see text] of the two Markov traces coincide.

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22

Henniart, Guy, and Bertrand Lemaire. "Intégrales orbitales tordues sur GL(n, F) et corps locaux proches : applications." Canadian Journal of Mathematics 58, no. 6 (December 1, 2006): 1229–67. http://dx.doi.org/10.4153/cjm-2006-044-5.

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RésuméSoient F un corps commutatif localement compact non archimédien, G = GL(n, F) pour un entier n ≥ 2, et κ un caractère de F× trivial sur (F×)n. On prouve une formule pour les κ-intégrales orbitales régulières sur G permettant, si F est de caractéristique > 0, de les relever à la caractéristique nulle. On en déduit deux résultats nouveaux en caractéristique à 0 : le “lemme fondamental” pour l’induction automorphe, et une version simple de la formule des traces tordue locale d’Arthur reliant κ-intégrales orbitales elliptiques et caractères κ-tordus. Cette formule donne en particulier, pour une série κ-discrète de G, les κ-intégrales orbitales elliptiques d’un pseudo-coefficient comme valeurs du caractère κ-tordu.

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23

LIEB, ELLIOTT H., and GERT K. PEDERSEN. "CONVEX MULTIVARIABLE TRACE FUNCTIONS." Reviews in Mathematical Physics 14, no. 07n08 (July 2002): 631–48. http://dx.doi.org/10.1142/s0129055x02001260.

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For any densely defined, lower semi-continuous trace τ on a C*-algebra A with mutually commuting C*-subalgebras A1, A2, … An, and a convex function f of n variables, we give a short proof of the fact that the function (x1, x2, …, xn)→ τ (f (x1, x2, …, xn)) is convex on the space [Formula: see text]. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called ℓ-convexity, show how it applies to traces, and give some examples. In particular we show that the Kadison–Fuglede determinant is concave and that the trace of an operator mean is always dominated by the corresponding mean of the trace values.

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24

Scholl, A. J. "A trace formula forF-crystals." Inventiones Mathematicae 79, no. 1 (February 1985): 31–48. http://dx.doi.org/10.1007/bf01388655.

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25

Buslaev, V. S., and E. A. Rybakina. "Trace formula in Hamiltonian mechanics." Journal of Soviet Mathematics 28, no. 5 (March 1985): 645–59. http://dx.doi.org/10.1007/bf02112328.

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26

Guillemin, Victor, and Alejandro Uribe. "Reduction and the trace formula." Journal of Differential Geometry 32, no. 2 (1990): 315–47. http://dx.doi.org/10.4310/jdg/1214445310.

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27

Waltner, Daniel, Petr Braun, Maram Akila, and Thomas Guhr. "Trace formula for interacting spins." Journal of Physics A: Mathematical and Theoretical 50, no. 8 (January 18, 2017): 085304. http://dx.doi.org/10.1088/1751-8121/aa5533.

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28

SCHWARZ, A. S. "LEFSCHETZ TRACE FORMULA AND BRST." Modern Physics Letters A 04, no. 20 (October 10, 1989): 1891–97. http://dx.doi.org/10.1142/s0217732389002148.

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29

Fang, Jiangxue. "Equivariant trace formula mod p." Comptes Rendus Mathematique 354, no. 4 (April 2016): 335–38. http://dx.doi.org/10.1016/j.crma.2015.12.014.

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30

Creagh, Stephen C. "Trace Formula for Broken Symmetry." Annals of Physics 248, no. 1 (May 1996): 60–94. http://dx.doi.org/10.1006/aphy.1996.0051.

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31

Bombara, Giuseppe, and Calin Belta. "Offline and Online Learning of Signal Temporal Logic Formulae Using Decision Trees." ACM Transactions on Cyber-Physical Systems 5, no. 3 (July 2021): 1–23. http://dx.doi.org/10.1145/3433994.

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In this article, we focus on inferring high-level descriptions of a system from its execution traces. Specifically, we consider a classification problem where system behaviors are described using formulae of Signal Temporal Logic (STL). Given a finite set of pairs of system traces and labels, where each label indicates whether the corresponding trace exhibits some system property, we devised a decision-tree-based framework that outputs an STL formula that can distinguish the traces. We also extend this approach to the online learning scenario. In this setting, it is assumed that new signals may arrive over time and the previously inferred formula should be updated to accommodate the new data. The proposed approach presents some advantages over traditional machine learning classifiers. In particular, the produced formulae are interpretable and can be used in other phases of the system’s operation, such as monitoring and control. We present two case studies to illustrate the effectiveness of the proposed algorithms: (1) a fault detection problem in an automotive system and (2) an anomaly detection problem in a maritime environment.

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32

Langlands, Robert P. "Un nouveau point de repère dans la théorie des formes automorphes." Canadian Mathematical Bulletin 50, no. 2 (June 1, 2007): 243–67. http://dx.doi.org/10.4153/cmb-2007-026-4.

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Ceux qui connaissent l’auteur et ses écrits, comme par exemple [L1] et [L2], savent que la notion de fonctorialité et les conjectures rattachées à celle-ci ont été introduites —en suivant ce que Artin avait fait pour un ensemble plus restreint de fonctions— pour aborder le problème de la prolongation analytique générale des fonctions L-automorphes. Ils savent en plus que je suis d’avis que seules les méthodes basées sur la formule des traces pourront aller au fond des problèmes. Il n’en reste pas moins que malgré de récents progrès importants sur le lemme fondamental et la formule des traces nous sommes bien loin de notre but.

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33

ROGERS, Carl R. "Et après?" Sociologie et sociétés 9, no. 2 (September 30, 2002): 55–67. http://dx.doi.org/10.7202/001654ar.

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Résumé L'auteur trace un bref aperçu des nouveaux problèmes auxquels a ou aura à faire face un enseignement humain et innovateur, alors qu'il devient de plus en plus une force importante dans le système d'enseignement. Il esquisse quelques-uns des défis auxquels sera confronté l'enseignant en tant que personne, au fur et à mesure que l'enseignement innovateur se développera. Dans le domaine de la recherche, il présente quelques découvertes récentes, toutes trop peu connues et formule aussi l'espoir que la recherche actuelle ne se limite pas à la simple évaluation, mais qu'elle étudie assidûment des rapports de nature "si-alors". Enfin, il spécule sur la prochaine grande frontière de l'apprentissage qui pourrait bien avoir trait à deux des facultés les moins valorisées dans notre culture : soit nos pouvoirs psychiques et intuitifs.

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34

Garfinkel, Irwin, Robert Haveman, and Lorne Huston. "Les politiques américaines contre la pauvreté : quelques propositions." II. La critique néo-libérale contemporaine et les limites d’intervention étatique, no. 16 (January 12, 2016): 77–93. http://dx.doi.org/10.7202/1034399ar.

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L’article trace l’évolution des politiques de lutte contre la pauvreté depuis 1965. Il décrit ensuite, statistiques à l’appui, les effets des politiques de transferts de revenu sur la pauvreté, l’insécurité et l’inégalité économique, puis sur le travail, l’épargne et la famille. Il établit que les politiques de transferts de revenu ont contribué à réduire la pauvreté et les inégalités mais qu’elles n’ont eu qu’un effet palliatif et provisoire. Elles n’ont pas réussi à augmenter la participation des pauvres au marché du travail. Promouvoir une telle participation exige une intervention sur plusieurs fronts : l’éducation, la qualification professionnelle, les politiques de soutien du revenu, etc. Aucune formule simple ou appliquée de façon isolée ne peut avoir d’impact significatif sur le problème. Les auteurs formulent une série de propositions susceptibles de renforcer la lutte contre la pauvreté.

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35

Chaudouard, Pierre-Henri. "Sur certaines contributions unipotentes dans la formule des traces d'Arthur." American Journal of Mathematics 140, no. 3 (2018): 699–752. http://dx.doi.org/10.1353/ajm.2018.0017.

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36

Zydor, Michał. "Les formules des traces relatives de Jacquet–Rallis grossières." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 762 (May 1, 2020): 195–259. http://dx.doi.org/10.1515/crelle-2018-0027.

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AbstractOn établit les formules des traces relatives de Jacques–Rallis grossières pour les groupes linéaires et unitaires. Les deux formules sont sous la forme suivante: une somme des distributions spectrales est égale à une somme des distributions géométriques. Pour établir les développements spectraux on introduit de nouveaux opérateurs de troncature et on étudie leur propriétés. Du côté géométrique, en utilisant les applications de Cayley, les développements s’obtiennent par un argument de descente vers les espaces tangents pour lesquels les formules sont connues grâce à nos travaux précédents.We establish the coarse relative trace formulae of Jacquet–Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral decompositions we introduce new truncation operators and we investigate their properties. On the geometric side, by means of the Cayley transform, the decompositions are derived from a procedure of descent to the tangent spaces for which the formulae are known thanks to our previous work.

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37

RAULF, NICOLE, and OLIVER STEIN. "A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS." Glasgow Mathematical Journal 59, no. 1 (June 10, 2016): 143–65. http://dx.doi.org/10.1017/s0017089516000094.

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AbstractWe present a ready to compute trace formula for Hecke operators on vector-valued modular forms of integral weight for SL2(ℤ) transforming under the Weil representation. As a corollary, we obtain a ready to compute dimension formula for the corresponding space of vector-valued cusp forms, which is more general than the dimension formulae previously published in the vector-valued setting.

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38

Chō, Muneo, and Tadasi Huruya. "Trace formulae for p-hyponormal operators." Studia Mathematica 161, no. 1 (2004): 1–18. http://dx.doi.org/10.4064/sm161-1-1.

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39

Müller, Werner, Sug Woo Shin, Birgit Speh, and Nicolas Templier. "Harmonic Analysis and the Trace Formula." Oberwolfach Reports 14, no. 2 (April 27, 2018): 1551–630. http://dx.doi.org/10.4171/owr/2017/25.

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40

Mehlig, Bernhard, and Michael Wilkinson. "Semiclassical trace formulae using coherent states." Annalen der Physik 513, no. 6-7 (June 2001): 541–59. http://dx.doi.org/10.1002/andp.200151306-705.

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41

Sinha, Kalyan B., and A. N. Mohapatra. "Spectral shift function and trace formula." Proceedings / Indian Academy of Sciences 104, no. 4 (November 1994): 819–53. http://dx.doi.org/10.1007/bf02830804.

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42

CHŌ, Muneo, and Tadasi HURUYA. "Trace Formula for Partial Isometry Case." Tokyo Journal of Mathematics 32, no. 1 (June 2009): 27–32. http://dx.doi.org/10.3836/tjm/1249648407.

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43

Guillemin, V., and A. Uribe. "The trace formula for vector bundles." Bulletin of the American Mathematical Society 15, no. 2 (October 1, 1986): 222–25. http://dx.doi.org/10.1090/s0273-0979-1986-15482-0.

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44

Sano, Mitsusada M. "Trace formula of quantum Liouville operator." Physical Review E 59, no. 4 (April 1, 1999): R3795—R3798. http://dx.doi.org/10.1103/physreve.59.r3795.

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45

Jacquet, Herv�, King F. Lai, and Stephen Rallis. "A trace formula for symmetric spaces." Duke Mathematical Journal 70, no. 2 (May 1993): 305–72. http://dx.doi.org/10.1215/s0012-7094-93-07006-8.

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46

Mao, Zhengyu, and Stephen Rallis. "A trace formula for dual pairs." Duke Mathematical Journal 87, no. 2 (March 1997): 321–41. http://dx.doi.org/10.1215/s0012-7094-97-08712-3.

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47

Nenciu, Irina. "A note on circular trace formulae." Proceedings of the American Mathematical Society 136, no. 08 (April 8, 2008): 2785–92. http://dx.doi.org/10.1090/s0002-9939-08-09132-6.

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48

Yang, Rongwei. "A trace formula for isometric pairs." Proceedings of the American Mathematical Society 131, no. 2 (June 5, 2002): 533–41. http://dx.doi.org/10.1090/s0002-9939-02-06687-x.

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49

Gornet, Ruth. "Riemannian nilmanifolds and the trace formula." Transactions of the American Mathematical Society 357, no. 11 (June 10, 2005): 4445–79. http://dx.doi.org/10.1090/s0002-9947-05-03965-6.

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50

Labesse, J. P. "STABLE TWISTED TRACE FORMULA: ELLIPTIC TERMS." Journal of the Institute of Mathematics of Jussieu 3, no. 4 (September 8, 2004): 473–530. http://dx.doi.org/10.1017/s1474748004000143.

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This paper deals with the stabilization of the contribution of elliptic elements to the geometric side of the general twisted trace formula. We extend the results of Langlands, Kottwitz and Shelstad to all elliptic elements for the general twisted trace formula.AMS 2000 Mathematics subject classification: Primary 11F72; 11R39; 11R34

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