본문 바로가기
KERD
논문KCI 등재

Fixed point theorems for infinite dimensional holomorphic functions

Lawrence A. Harris
대한수학회 (The Korean Mathematical Society)|2004.01|대한수학회지 (Journal of the KMS)|제41권 제1호|pp. 175-192

0

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan’s uniqueness theorem.

참고문헌 (23)

  1. "Shoikhet,One-sided estimates for the existence ofnull points of holomorphic mappings in Banach spaces", 203, pp.38~54 (1996)
  2. "Numerical Ranges of Operators on Normed Spacesand of Elements of Normed Algebras" (1971), Cambridge Univ. Press
  3. "Local uniform linear convexity with respect to the Kobayashi dis-tance", (6), pp.367~373 (2003)
  4. "Complex Analysis in Localy Convex Spaces" (1981), North-Holland
  5. "Complex Analysis on Innite-dimensional Spaces" (1999), J. Math. Anal. Appl
  6. "A xed point theorem for holomorphic mappings", 16, pp.6165~ (1970)
  7. "Schwarzs lemma andthe Kobayashi and Caratheodory metrics on complex Banach manifolds", Cambridge Univ. Press
  8. "A continuous form of Schwarzs lemma in normed linear spaces", 38 (1971)
  9. "The numerical range of holomorphic functions in Banach spaces", 93 (1971)
  10. "On the size of balls covered by analytic transformations", 83, pp.923~ (1977)
  11. "Schwarz-Pick systems of pseudometrics for domains in normed linearspaces in Advances in Holomorphy" (1979), North-Holland
  12. "Fixed points of holomorphic mappings for domains in Banach spaces", (5), pp.261~274 (2003)
  13. "Dissipative holomorphic functions", 82, pp.221~232 (2000)
  14. "Fixed points of holomorphic maps in Banachspaces", 60, pp.95105~ (1976)
  15. "Topological properties of the unit sphere of a Hilbert space", 19 (1943)
  16. "Fixed point theorems for holomor-phic mappings and operator theory in indenite metric spaces", 22, pp.305~316 (1995)
  17. "Common xed points of commuting holomorphic mappings inHilbert ball and polydisc", 8 (1984)
  18. "Nonexpansive retracts and xed points of nonexpansive mappings in theCartesian product ofn Hilbert balls", 9 (1985)
  19. "Fixed points of holomorphic mappings", pp.437~515 (2001)
  20. "Semi-inner-product spaces", 100, pp.2943~ (1961)
  21. "Generation theory for semigroups of holomorphic mappingsin Banach spaces", 1, pp.1~44 (1996)
  22. "Bolzano？s theorem in several complex variables", 79 (1980)
  23. "The Theory of Functions" (1939)

관련 논문AI추천

Spectral theory, tensor products and infinite dimensional holomorphySe\'an Dineen대한수학회 · 대한수학회지2004 · 제41권 제1호Holomorphic mappings into some domain in a complex normed spaceTatsuhiro Honda대한수학회 · 대한수학회지2004 · 제41권 제1호Holomorphic embeddings of Stein spaces in infinite-dimensional projective spacesE. Ballico대한수학회 · 대한수학회지2005 · 제42권 제1호Holomorphic functions and the BB-property on product spacesChristopher Boyd대한수학회 · 대한수학회지2004 · 제41권 제1호Remarks on Fixed Point Theorems of Non-Lipschitzian Self-mappingsByung-Ik Jeon, Tae-Hwa Kim경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제3호Zeros of real polynomials on Banach spacesJos{\'e} G. Llavona대한수학회 · 대한수학회지2004 · 제41권 제1호

이 간행물의 다른 논문 (14건)

Composition operators on uniform algebras and the pseudohyperbolic metricT. W. Gamelin, P. Galindo, M. Lindstr\pp. 1-20Functions attaining the supremum and isomorphic properties of a Banach spaceManuel Ruiz, Julio Becerra Guerrero, Mar\'{\i}a D. Acostapp. 21-38Holomorphic functions and the BB-property on product spacesChristopher Boydpp. 39-50Properties of Q-reflexive locally convex spacesMilena Venkovapp. 51-64On universal functionsDinesh Markose, Richard Aronpp. 65-76
원문 보기