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Relevant bibliographies by topics / Lemme de Schwartz

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Academic literature on the topic 'Lemme de Schwartz'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Lemme de Schwartz"

1

Boivin, Daniel. "Théorèmes de Convergence Locale Pour Les Résolvantes et Les Processus Abéliens à Plusieurs Paramètres." Canadian Journal of Mathematics 39, no. 5 (October 1, 1987): 1147–61. http://dx.doi.org/10.4153/cjm-1987-058-2.

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En démontrant un lemme ergodique maximal pour une famille résolvante de contractions positives et propres de L1(σ) [5], D. Feyel a obtenu, entre autres, des théorèmes de dérivation pour les processus abéliens [7]. Grâce à un théorème taubérien, il peut déduire un théorème de convergence locale pour les processus additifs. Le but de cet article est de montrer que le lemme ergodique maximal de D. Feyel et une technique de réduction des paramètres, introduite par Dunford-Schwartz [4] et développée par Terrell [13] et Akcoglu-del Junco [1] permettent d'obtenir des théorèmes de dérivation pour les familles résolvantes à plusieurs paramètres. C'est ce qu'on fait à la Section 2. Le premier théorème ergodique local pour les semi-groupes de contractions a été obtenu par Krengel [10] et Ornstein [12]. A la Section 3, nous considérons les processus abéliens associés aux processus additifs qui ont été introduits dans [2] par Akcoglu et Krengel et dont les résultats ont ensuite été généralisés par Terrell [13], Akcoglu et del Junco [1], Emilion [5]. Comme dans le cas à un paramètre, à la Section 4, nous retrouvons un théorème local pour les processus additifs.

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Zhu, Jian-Feng. "Schwarz lemma and boundary Schwarz lemma for pluriharmonic mappings." Filomat 32, no. 15 (2018): 5385–402. http://dx.doi.org/10.2298/fil1815385z.

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In this paper, we first improve the boundary Schwarz lemma for holomorphic self-mappings of the unit ball Bn, and then we establish the boundary Schwarz lemma for harmonic self-mappings of the unit disk D and pluriharmonic self-mappings of Bn. The results are sharp and coincides with the classical boundary Schwarz lemma when n = 1.

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3

Yamashita, Shinji. "Sur le Lemme de Schwarz." Canadian Mathematical Bulletin 28, no. 2 (June 1, 1985): 233–36. http://dx.doi.org/10.4153/cmb-1985-028-4.

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Huang, Ziyan, Di Zhao, and Hongyi Li. "A boundary Schwarz lemma for pluriharmonic mappings between the unit polydiscs of any dimensions." Filomat 34, no. 9 (2020): 3151–60. http://dx.doi.org/10.2298/fil2009151h.

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In this paper, we present a boundary Schwarz lemma for pluriharmonic mappings between the unit polydiscs of any dimensions, which extends the classical Schwarz lemma for bounded harmonic functions to higher dimensions.

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5

Mateljevic, Miodrag, and Marek Svetlik. "Hyperbolic metric on the strip and the Schwarz lemma for HQR mappings." Applicable Analysis and Discrete Mathematics 14, no. 1 (2020): 150–68. http://dx.doi.org/10.2298/aadm200104001m.

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We give simple proofs of various versions of the Schwarz lemma for real valued harmonic functions and for holomorphic (more generally harmonic quasiregular, shortly HQR) mappings with the strip codomain. Along the way, we get a simple proof of a new version of the Schwarz lemma for real valued harmonic functions (without the assumption that 0 is mapped to 0 by the corresponding map). Using the Schwarz-Pick lemma related to distortion for harmonic functions and the elementary properties of the hyperbolic geometry of the strip we get optimal estimates for modulus of HQR mappings.

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6

Gramain, François. "Lemme de Schwarz pour des produits cartésiens." Annales mathématiques Blaise Pascal 8, no. 2 (2001): 67–75. http://dx.doi.org/10.5802/ambp.142.

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7

Besson, Gérard, Gilles Courtois, and Sylvestre Gallot. "Lemme de Schwarz réel et applications géométriques." Acta Mathematica 183, no. 2 (1999): 145–69. http://dx.doi.org/10.1007/bf02392826.

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8

Pal, Sourav, and Samriddho Roy. "A generalized Schwarz lemma for two domains related to μ-synthesis." Complex Manifolds 5, no. 1 (February 2, 2018): 1–8. http://dx.doi.org/10.1515/coma-2018-0001.

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AbstractWe present a set of necessary and sufficient conditions that provides a Schwarz lemma for the tetrablock E. As an application of this result, we obtain a Schwarz lemma for the symmetrized bidisc G2. In either case, our results generalize all previous results in this direction for E and G2.

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Edigarian, Armen, and Włodzimierz Zwonek. "Schwarz lemma for the tetrablock." Bulletin of the London Mathematical Society 41, no. 3 (March 22, 2009): 506–14. http://dx.doi.org/10.1112/blms/bdp022.

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Ratto, Andrea, Marco Rigoli, and Laurent Veron. "extensions of the Schwarz Lemma." Duke Mathematical Journal 74, no. 1 (April 1994): 223–36. http://dx.doi.org/10.1215/s0012-7094-94-07411-5.

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Dissertations / Theses on the topic "Lemme de Schwartz"

1

Rivard, Patrice. "Un lemme de Schwartz-Pick à points multiples." Master's thesis, Université Laval, 2007. http://hdl.handle.net/20.500.11794/19410.

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Khémira, Samy. "Approximants de Hermite-Padé, déterminants d'interpolation et approximation diophantienne." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/tel-00009653.

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Cette thèse aborde des sujets d'approximation diophantienne et de transcendance liés aux fonctions exponentielles. Il est tout d'abord établit des liens entre les coefficients d'approximants de Hermite-Padé, ceux de polynômes d'interpolation de Hermite et certains cofacteurs d'un déterminant de Vandermonde généralisé. Nous utilisons ensuite la notion de hauteur d'une matrice (que nous majorons grâce aux liens précédemment fournis) afin de donner une nouvelle démonstration de la transcendance de $e$. Ces résultats nous permettent finalement d'obtenir de nouveaux énoncés d'approximation diophantienne tels que la minoration de la distance de l'exponentielle d'un nombre algébrique (de hauteur absolue logarithmique de Weil bornée) à un autre nombre algébrique (lui aussi de hauteur absolue logarithmique de Weil bornée) en fonction de ces mêmes bornes. Il est ensuite donné, pour différentes valeurs de nombres rationnels $a$, quelques estimations remarquables telles que le minimum, sur l'ensemble des entiers non nuls $b$ et $c$, de la distance $|e^(b)-a^(c)|$.

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Rivard, Patrice. "Un lemme de Schwarz-Pick à points multiples." Thesis, Université Laval, 2007. http://www.theses.ulaval.ca/2007/24845/24845.pdf.

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Schwartz, Stefanie [Verfasser], and Karsten [Akademischer Betreuer] Lemmer. "Sicherheitsschichten im Eisenbahnsystem / Stefanie Schwartz ; Betreuer: Karsten Lemmer." Braunschweig : Technische Universität Braunschweig, 2012. http://d-nb.info/1175823066/34.

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Nokrane, Abdelkrim. "Le lemme de Schwarz pour les multifonctions analytiques finies et applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0001/NQ43100.pdf.

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Terenzi, Gloria. "Lemma di Schwarz e la sua interpretazione geometrica." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13543/.

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Il tema centrale di questa tesi, suddivisa in tre capitoli, è il Lemma di Schwarz e la sua applicazione nella geometria iperbolica. Il lemma di Schwarz, che prende il nome da Hermann Amandus Shchwarz, descrive una proprietà delle funzioni olomorfe. Nel primo capitolo enuncio il Lemma di Schwarz e la sua versione infinitesimale. Descrivo le mappe conformi del dominio per poi applicare il lemma di Pick che è una forma particolare del lemma di Schwarz.Nel secondo capitolo introduco brevemente la geometria euclidea con i cinque postulati di Euclide, per poi passare a descrivere la geometria iperbolica. Introduco la definizione di forma fondamentale (o forma metrica) di una superficie. Nel terzo capitolo affronto la geometria iperbolica nel disco. Quindi data una forma metrica ho definito distanza iperbolica e lunghezza iperbolica per poi arrivare a dimostrare tramite una reinterpretazione del lemma di Schwarz l'invarianza delle mappe olomorfe.

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Imechrane, Meriem. "Applications harmoniques : singularités apparentes, lemme de Schwarz-Yau et grand théorème de Picard." Corté, 2012. http://www.theses.fr/2012CORT0027.

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Le premier but de ce travail est de donner des preuves « réelles » du grand théorème de Picard et d’un théorème voisin de Myung Kwack. Par « réelles » nous voulons dire n’utilisant pas d’analyse complexe, particulièrement la partie qui repose sur le théorème de Cauchy. Ce programme est facilement mené à bien à l’aide d’un théorème de J. Sacks et K. Uhlenbeck et d’une large généralisation du lemme de Schwarz-Pick de la théorie des fonctions classique, à savoir le lemme de Schwarz-Yau. Le principal résultat obtenu ainsi est la version réelle suivante du théorème de Kwack. (. . . /. . . )
The first aim of this work is to provide ʺrealʺ proofs of the Big Picard Theorem and of a related theorem of Myung Kwack. By ʺreal" we mean : without using complex analysis, especially that part relying on the Cauchy Theorem. This program is easily carried out with the help of a theorem of J. Sacks and K. Uhlenbeck and a huge generalization of the Schwarz-Pick Lemma of classical function theory, namely the Schwarz-Yau Lemma. The main result so acheved is the following real version of Kwack’s theorem. (. . . /. . . )

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Bacca, Salvatore. "Il lemma di Schwarz e la distanza di Kobayashi." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13823/.

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Questa tesi è un approccio elementare alla teoria geometrica delle funzioni, campo che ebbe inizio con i lavori di Poincarè sulla geometria del disco. Affronteremo dapprima il Lemma di Schwarz ed alcune sue generalizzazioni che metteranno in correlazione il risultato analitico di tale asserto con il suo aspetto geometrico-differenziale. Introdurremo poi una distanza invariante su varietà complesse, la distanza di Kobayashi, e tramite questa dimostreremo i teoremi di Picard riguardanti il range dell'immagine di funzioni olomorfe sul piano complesso o su un dominio avente una singolarità isolata.

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Barros, Jéssica Laís Calado de. "O teorema da aplicação de Riemann: uma prova livre de integração." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-13122017-161946/.

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Neste trabalho, seguindo a abordagem de Weierstrass, temos o objetivo de responder a seguinte questão: conhecida a equivalência entre holomorfia e analiticidade no caso complexo, quais propriedades das funções analíticas podem ser obtidas sem assumir tal equivalência? Analisando esta situação, resultados interessantes serão obtidos sem o uso de qualquer teorema de integração complexa e, para alcançar tal objetivo, nossas principais ferramentas serão a teoria de somas não ordenadas de famílias em C e propriedades do índice de caminhos fechados. Entre os resultados apresentados estão os conhecidos Teorema Fundamental da Álgebra, Lema de Schwarz, Teorema de Montel, Teorema da Série Dupla de Weierstrass, Princípio do Argumento, Teorema de Rouché, Teorema da Fatoração de Weierstrass, Pequeno Teorema de Picard e o Teorema da Aplicação de Riemann.
In this work, following the Weierstrass\'s approach, we aim to answer the following question: knowing the equivalence between holomorphy and analyticity in the complex case, which properties of analytic functions can be obtained without assuming such equivalence? Through analyzing this situation, interesting results will be obtained without employing of any complex integration theorem and in order to achieve this goal, our main tools will be the theory of unordered sums in C and properties of winding numbers of closed paths. Among the proven results are the well known Fundamental Theorem of Algebra, Schwarz\'s Lemma, Montel\'s Theorem, Weierstrass\'s Double Series Theorem, Argument Principle, Rouché\'s Theorem, Weierstrass\'s Factorization Theorem, Picard\'s Little Theorem and the Riemann\'s Mapping Theorem.

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10

Rivard, Patrice. "Un lemme de Schwartz-Pick à points multiples /." 2007. http://www.theses.ulaval.ca/2007/24845/24845.pdf.

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Books on the topic "Lemme de Schwartz"

1

Dineen, Seán. The Schwarz lemma. Mineola, New York: Dover Publications, 2016.

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2

The Schwarz lemma. Oxford: Clarendon Press, 1989.

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3

Kim, Kang-Tae. Schwarz's lemma from a differential geometric viewpoint. Singapore: World Scientific, 2011.

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Book chapters on the topic "Lemme de Schwartz"

1

Kodaira, Kunihiko. "Schwarz–Kobayashi Lemma." In SpringerBriefs in Mathematics, 19–38. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6787-7_2.

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Kobayashi, Shoshichi. "Schwarz Lemma and Negative Curvature." In Grundlehren der mathematischen Wissenschaften, 19–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03582-5_2.

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3

Elin, Mark, Fiana Jacobzon, Marina Levenshtein, and David Shoikhet. "The Schwarz Lemma: Rigidity and Dynamics." In Harmonic and Complex Analysis and its Applications, 135–230. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01806-5_3.

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4

Gamelin, Theodore W. "The Schwarz Lemma and Hyperbolic Geometry." In Undergraduate Texts in Mathematics, 260–73. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-0-387-21607-2_9.

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Moriya, Katsuhiro. "The Schwarz Lemma for Super-Conformal Maps." In Hermitian–Grassmannian Submanifolds, 59–68. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5556-0_6.

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6

Burgeth, Bernhard. "Schwarz Lemma Type Inequalities for Harmonic Functions in the Ball." In Classical and Modern Potential Theory and Applications, 133–47. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1138-6_13.

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Muller, Marie-Paule. "Gromov’s Schwarz lemma as an estimate of the gradient for holomorphic curves." In Holomorphic Curves in Symplectic Geometry, 217–31. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8508-9_8.

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Yuan, Xinyi, Shou-Wu Zhang, and Wei Zhang. "Assumptions on the Schwartz Function." In The Gross-Zagier Formula on Shimura Curves. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691155913.003.0005.

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This chapter introduces two classes of degenerate Schwartz functions which significantly simplify the computations and arguments of both the analytic kernel and the geometric kernel functions. It first restates the kernel identity in terms of un-normalized kernel functions before stating the assumptions on the Schwartz function and claiming that these assumptions can be “added” to the kernel identity without losing the generality. It then considers some simple properties of the assumptions and proceeds by discussing the two classes of degenerate Schwartz functions. In the first case, a non-archimedean local field and a non-degenerate quadratic space are described. In the second case, since all the data are unramified, the lemma can be verified by explicit computations.

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"Distance and the Schwarz Lemma." In Hyperbolic Manifolds and Holomorphic Mappings, 37–43. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812775054_0003.

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"Consequences of the Schwarz Lemma." In Function Theory in the Unit Ball of ℂn, 161–84. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-3-540-68276-9_8.

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Conference papers on the topic "Lemme de Schwartz"

1

ALIYEV AZEROĞLU, T., and BÜLENT N. ÖRNEK. "A GENERALIZED SCHWARTZ LEMMA AT THE BOUNDARY." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0009.

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Akyel, Tuğba, and Bülent Nafi Örnek. "On the rigidity part of Schwarz Lemma." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136123.

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