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Journal articles on the topic 'Lemme de Schwartz'

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Published: 4 June 2021

Last updated: 1 February 2022

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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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2

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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4

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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9

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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10

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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11

Yang, Yan, and Tao Qian. "Schwarz lemma in Euclidean spaces." Complex Variables and Elliptic Equations 51, no. 7 (July 2006): 653–59. http://dx.doi.org/10.1080/17476930600688623.

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12

Xu, Zhenghua. "Schwarz lemma for pluriharmonic functions." Indagationes Mathematicae 27, no. 4 (September 2016): 923–29. http://dx.doi.org/10.1016/j.indag.2016.06.002.

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13

KALAJ, DAVID. "SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL." Glasgow Mathematical Journal 60, no. 1 (September 4, 2017): 219–24. http://dx.doi.org/10.1017/s0017089517000052.

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AbstractIn this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls Bn and Bm in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

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14

Hamada, Hidetaka. "A Schwarz lemma on complex ellipsoids." Annales Polonici Mathematici 67, no. 3 (1997): 269–75. http://dx.doi.org/10.4064/ap-67-3-269-275.

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15

Zhang, Zhongxiang. "The Schwarz lemma in Clifford analysis." Proceedings of the American Mathematical Society 142, no. 4 (January 6, 2014): 1237–48. http://dx.doi.org/10.1090/s0002-9939-2014-11854-5.

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16

Beardon, A. F. "The Schwarz-Pick Lemma for derivatives." Proceedings of the American Mathematical Society 125, no. 11 (1997): 3255–56. http://dx.doi.org/10.1090/s0002-9939-97-03906-3.

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17

Örnek, Nafi, and Burcu Gök. "Boundary Schwarz lemma for holomorphic functions." Filomat 31, no. 18 (2017): 5553–65. http://dx.doi.org/10.2298/fil1718553o.

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In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f (z) holomorphic in the unit disc and f (0) = 0 such that ?Rf? < 1 for ?z? < 1, we estimate a modulus of angular derivative of f (z) function at the boundary point b with f (b) = 1, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ?f'(b)? according to the first nonzero Taylor coefficient of about two zeros, namely z=0 and z0 ? 0. Moreover, two examples for our results are considered.

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18

Krantz, Steven G. "The Schwarz lemma at the boundary." Complex Variables and Elliptic Equations 56, no. 5 (May 2011): 455–68. http://dx.doi.org/10.1080/17476931003728438.

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19

Mercer, Peter R. "Sharpened Versions of the Schwarz Lemma." Journal of Mathematical Analysis and Applications 205, no. 2 (January 1997): 508–11. http://dx.doi.org/10.1006/jmaa.1997.5217.

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20

Knese, Greg. "A Schwarz lemma on the polydisk." Proceedings of the American Mathematical Society 135, no. 09 (March 30, 2007): 2759–69. http://dx.doi.org/10.1090/s0002-9939-07-08766-7.

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21

Klimek, M. "Infinitesimal pseudometrics and the Schwarz lemma." Proceedings of the American Mathematical Society 105, no. 1 (January 1, 1989): 134. http://dx.doi.org/10.1090/s0002-9939-1989-0930248-4.

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22

Ito, Manabu. "Schwarz Lemma in infinite-dimensional spaces." Monatshefte für Mathematik 191, no. 4 (January 29, 2020): 735–48. http://dx.doi.org/10.1007/s00605-020-01375-x.

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23

Dineen, Seán, and Richard M. Timoney. "Extremal mappings for the Schwarz lemma." Arkiv för Matematik 30, no. 1-2 (December 1992): 61–81. http://dx.doi.org/10.1007/bf02384862.

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24

Mackey, M., and P. Mellon. "A Schwarz Lemma and Composition Operators." Integral Equations and Operator Theory 48, no. 4 (April 1, 2004): 511–24. http://dx.doi.org/10.1007/s00020-003-1240-1.

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25

Beardon, A. F., and D. Minda. "A multi-point Schwarz-Pick Lemma." Journal d'Analyse Mathématique 92, no. 1 (December 2004): 81–104. http://dx.doi.org/10.1007/bf02787757.

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26

Liu, Bingyuan. "Two applications of the Schwarz lemma." Pacific Journal of Mathematics 296, no. 1 (May 1, 2018): 141–53. http://dx.doi.org/10.2140/pjm.2018.296.141.

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27

Charpentier, S., and L. Deleaval. "On a vector-valued Hopf–Dunford–Schwartz lemma." Positivity 17, no. 3 (October 27, 2012): 899–910. http://dx.doi.org/10.1007/s11117-012-0211-7.

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28

Vigué, Jean-Pierre. "Un lemme de Schwarz pour les boules-unités ouvertes." Canadian Mathematical Bulletin 40, no. 1 (March 1, 1997): 117–28. http://dx.doi.org/10.4153/cmb-1997-014-4.

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RésuméLet B1 and B2 be the open unit balls of ℂn1 and ℂn2 for the norms ‖. ‖1 and ‖ . ‖2. Let f: B1 → B2 be a holomorphic mapping such that f(0) = 0. It is well known that, for every z ∈ B1, ‖f(z)‖2 ≤ ‖z‖1, and ‖f′(0)‖ ≤ 1.In this paper, I prove the converse of this result. Let f : B1 → B2 be a holomorphic mapping such that f'(0) is an isometry. If B2 is strictly convex, I prove that f(0)=0 and that f is linear. I also define the rank of a point x belonging to the boundary of B1 or B2. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that f(0)=0 and that f'(0) is an isometry is linear.

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29

MOHAPATRA, MANAS RANJAN, XIANTAO WANG, and JIAN-FENG ZHU. "BOUNDARY SCHWARZ LEMMA FOR SOLUTIONS TO NONHOMOGENEOUS BIHARMONIC EQUATIONS." Bulletin of the Australian Mathematical Society 100, no. 3 (September 9, 2019): 470–78. http://dx.doi.org/10.1017/s0004972719000947.

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30

Kwon, Ern, Jinkee Lee, Gun Kwon, and Mi Kim. "A Refinement of Schwarz–Pick Lemma for Higher Derivatives." Mathematics 7, no. 1 (January 13, 2019): 77. http://dx.doi.org/10.3390/math7010077.

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In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita.

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31

Mishra, Akshaya Kumar. "Some applications of Schwarz Lemma for operators." International Journal of Mathematics and Mathematical Sciences 12, no. 2 (1989): 349–53. http://dx.doi.org/10.1155/s0161171289000402.

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32

Akyel, Tugba, and Bulent Nafi Ornek. "Applications of the Jack's lemma for the meromorphic functions at the boundary." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (October 14, 2019): 219–26. http://dx.doi.org/10.5269/bspm.v38i7.46633.

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In this paper, a boundary version of the Schwarz lemma for the class $\mathcal{% N(\alpha )}$ is investigated. For the function $f(z)=\frac{1}{z}% +a_{0}+a_{1}z+a_{2}z^{2}+...$ defined in the punctured disc $E$ such that $% f(z)\in \mathcal{N(\alpha )}$, we estimate a modulus of the angular derivative of the function $\frac{zf^{\prime }(z)}{f(z)}$ at the boundary point $c$ with $\frac{cf^{\prime }(c)}{f(c)}=\frac{1-2\beta }{\beta }$. Moreover, Schwarz lemma for class $\mathcal{N(\alpha )}$ is given.

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33

Bernal-González, L., and M. C. Calderón-Moreno. "Two hyperbolic Schwarz lemmas." Bulletin of the Australian Mathematical Society 66, no. 1 (August 2002): 17–24. http://dx.doi.org/10.1017/s0004972700020633.

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In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings on the unit disk with fixed multiplicity for the zero at the origin. This extends a recent result due to Beardon. A property of preserving hyperbolic distances also studied by Beardon is here completely characterised.

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34

Mercer, Peter R. "An improved Schwarz Lemma at the boundary." Open Mathematics 16, no. 1 (October 19, 2018): 1140–44. http://dx.doi.org/10.1515/math-2018-0096.

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35

Huang, Ziyan, Di Zhao, and Hongyi Li. "Boundary Schwarz lemma and rigidity property for holomorphic mappings of the unit polydisc in Cn." Filomat 34, no. 9 (2020): 2813–18. http://dx.doi.org/10.2298/fil2009813h.

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In this paper, we generalize the classical Schwarz lemma at the boundary from the unit disk D in the complex plane to the unit polydisc Dn in higher-dimensional complex space. Two boundary Schwarz lemmas for holomorphic mappings of Dn and corresponding rigidity properties are established without the restriction of the interior fixed point.

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36

Verma, K. "A Schwarz lemma for correspondences and applications." Publicacions Matemàtiques 47 (July 1, 2003): 373–87. http://dx.doi.org/10.5565/publmat_47203_04.

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37

Jeong, Moon-Ja. "THE SCHWARZ LEMMA AND BOUNDARY FIXED POINTS." Pure and Applied Mathematics 18, no. 3 (August 31, 2011): 275–84. http://dx.doi.org/10.7468/jksmeb.2011.18.3.275.

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38

AKYEL, TUGBA, and NAFI ORNEK. "A SHARP SCHWARZ LEMMA AT THE BOUNDARY." Pure and Applied Mathematics 22, no. 3 (August 31, 2015): 263–73. http://dx.doi.org/10.7468/jksmeb.2015.22.3.263.

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39

Klimek, M. "Infinitesimal Pseudo-Metrics and the Schwarz Lemma." Proceedings of the American Mathematical Society 105, no. 1 (January 1989): 134. http://dx.doi.org/10.2307/2046747.

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40

Cheung, Leung-Fu, and Pui-Fai Leung. "A Schwarz lemma for complete Riemannian manifolds." Bulletin of the Australian Mathematical Society 55, no. 3 (June 1997): 513–15. http://dx.doi.org/10.1017/s000497270003416x.

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We prove a Schwarz Lemma for conformal mappings between two complete Riemannian manifolds when the domain manifold has Ricci curvature bounded below in terms of its distance function. This gives a partial result to a conjecture of Chua.

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41

Mercer, Peter R. "Boundary Schwarz inequalities arising from Rogosinski's lemma." Journal of Classical Analysis, no. 2 (2018): 93–97. http://dx.doi.org/10.7153/jca-2018-12-08.

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42

Agler, J., and N. J. Young. "A Schwarz Lemma for the Symmetrized Bidisc." Bulletin of the London Mathematical Society 33, no. 2 (March 2001): 175–86. http://dx.doi.org/10.1112/blms/33.2.175.

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43

Beardon, Alan F., and Kenneth Stephenson. "The Schwarz-Pick Lemma for circle packings." Illinois Journal of Mathematics 35, no. 4 (December 1991): 577–606. http://dx.doi.org/10.1215/ijm/1255987673.

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44

Chelst, Dov. "A generalized Schwarz lemma at the boundary." Proceedings of the American Mathematical Society 129, no. 11 (June 6, 2001): 3275–78. http://dx.doi.org/10.1090/s0002-9939-01-06144-5.

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45

Kalaj, David, and Matti Vuorinen. "On harmonic functions and the Schwarz lemma." Proceedings of the American Mathematical Society 140, no. 1 (May 2, 2011): 161–65. http://dx.doi.org/10.1090/s0002-9939-2011-10914-6.

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46

Cho, Kyung Hyun, Seong-A. Kim, and Toshiyuki Sugawa. "On a Multi-Point Schwarz-Pick Lemma." Computational Methods and Function Theory 12, no. 2 (August 21, 2012): 483–99. http://dx.doi.org/10.1007/bf03321839.

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47

Savas-Halilaj, Andreas. "A Schwarz–Pick lemma for minimal maps." Annals of Global Analysis and Geometry 56, no. 2 (May 16, 2019): 193–201. http://dx.doi.org/10.1007/s10455-019-09663-y.

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48

Mazet, Pierre. "Principe du Maximum et Lemme de Schwarz a Valeurs Vectorielles." Canadian Mathematical Bulletin 40, no. 3 (September 1, 1997): 356–63. http://dx.doi.org/10.4153/cmb-1997-042-9.

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RésuméNous établissons un théorème pour les fonctions holomorphes à valeurs dans une partie convexe fermée. Ce théorème précise la position des coefficients de Taylor de telles fonctions et peut être considéré comme une généralisation des inégalités de Cauchy. Nous montrons alors comment ce théorème permet de retrouver des versions connues du principe du maximum et d’obtenir de nouveaux résultats sur les applications holomorphes à valeurs vectorielles.

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49

Momani, Shaher, and Samir Hadid. "Lyapunov stability solutions of fractional integrodifferential equations." International Journal of Mathematics and Mathematical Sciences 2004, no. 47 (2004): 2503–7. http://dx.doi.org/10.1155/s0161171204312366.

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Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equationsx(α)(t)=f(t,x(t))+∫t0tk(t,s,x(s))ds,0<α≤1, with the initial conditionx(α−1)(t0)=x0, have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.

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50

Joseph, James E., and Myung H. Kwack. "A Generalization of the Schwarz Lemma to Normal Selfaps of Complex Spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 1 (February 2000): 10–18. http://dx.doi.org/10.1017/s1446788700001543.

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