The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the ﬁxed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional ﬁxed-points set. The origin of our interest in this problem lies in holomorphic dynamics.
Abstract In 1963 Atiyah and Singer proved the famous Atiyah-Singer Index Theorem, which states, among other things, that the space of elliptic pseudodiﬀerential operators is such that the collection of operators with any given index forms a connected subset. Contained in this statement is the somewhat more specialized claim that the index of an elliptic operator must be invariant under suﬃciently small perturbations.
Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: A Bijective Proof of a Major Index Theorem of Garsia and Gessel...
This paper is a continuation of Feﬀerman’s program  for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg¨ kernels of the domains as o analogs of the heat kernel of Riemannian manifolds. In Riemannian (or conformal) geometry, the coeﬃcients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric; by integrating the coeﬃcients one obtains index theorems in various settings. ...
Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree
Collection of research reports best universities honored author. Two. Le Van Dung, a number average convergence theorem for two index array of random elements in Banach spaces with integrable conditions are ... Science (in Latin Scientia, meaning "knowledge "or" understanding ") is the efforts to implement the invention, and increased knowledge of the human understanding of how the operation of the physical world around them.
ON THE SOLVABILITY OF INITIAL-VALUE PROBLEMS FOR NONLINEAR IMPLICIT DIFFERENCE EQUATIONS
PHAM KY ANH AND HA THI NGOC YEN Received 18 February 2004
Our aim is twofold. First, we propose a natural deﬁnition of index for linear nonautonomous implicit diﬀerence equations, which is similar to that of linear diﬀerentialalgebraic equations. Then we extend this index notion to a class of nonlinear implicit diﬀerence equations and prove some existence theorems for their initial-value problems. 1.