scholarly journals The Dolbeault complex in infinite dimensions III. Sheaf cohomology in Banach spaces

2000 ◽  
Vol 142 (3) ◽  
pp. 579-603 ◽  
Author(s):  
László Lempert
Keyword(s):  
Banach Spaces ◽  
Sheaf Cohomology ◽  
Infinite Dimensions ◽  
Dolbeault Complex

scholarly journals An example on composite differentiable functions in infinite dimensions

1989 ◽  
Vol 40 (1) ◽  
pp. 91-95 ◽  
Author(s):  
J.A. Jaramillo
Keyword(s):  
Banach Spaces ◽  
Classical Result ◽  
Infinite Dimensions ◽  
Differentiable Functions ◽  
Infinitely Differentiable Functions

We present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differentiable functions cannot be extended to the case of weakiy uniformly differentiable functions on Banach spaces.

The G-invariant implicit function theorem in infinite dimensions II

1986 ◽  
Vol 102 (3-4) ◽  
pp. 211-220 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Banach Spaces ◽  
Group Action ◽  
Implicit Function Theorem ◽  
Implicit Function ◽  
Infinite Dimensions ◽  
Regularity Theorem ◽  
Fredholm Maps

SynopsisIn this paper, we study the perturbation of zeros of maps of Banach spaces where the maps are invariant under continuous groups of symmetries. In some cases, we allow the perturbed maps partially to break the symmetries. Our results improve earlier results of the author by removing smoothness conditions on the group action. The key new idea is a regularity theorem for the zeros of invariant Fredholm maps.

A COMPARISON THEOREM FOR STOCHASTIC EQUATIONS IN INFINITE DIMENSIONS AND APPLICATIONS

2010 ◽  
Vol 10 (02) ◽  
pp. 197-210
Author(s):  
NIKOLAOS HALIDIAS ◽  
MARIUSZ MICHTA
Keyword(s):  
Existence Theorem ◽  
Banach Spaces ◽  
Comparison Theorem ◽  
Stochastic Equations ◽  
Dimensional Case ◽  
Infinite Dimensions ◽  
Infinite Dimensional ◽  
Drift Coefficient

In this paper we consider stochastic equations in Banach spaces. Our first result is a comparison theorem. As an application we prove an existence theorem in the case when the drift coefficient is nonsmooth. The present studies extend some results both for deterministic and stochastic equations in infinite dimensional case.

scholarly journals THE NORM OF THE PRODUCT OF POLYNOMIALS IN INFINITE DIMENSIONS

2006 ◽  
Vol 49 (1) ◽  
pp. 17-28 ◽  
Author(s):  
C. Boyd ◽  
R. A. Ryan
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Uniform Convexity ◽  
Analogous Problem ◽  
Homogeneous Polynomials ◽  
Infinite Dimensions ◽  
Multilinear Maps ◽  
Local Reflexivity ◽  
Positive Integers

AbstractGiven a Banach space $E$ and positive integers $k$ and $l$ we investigate the smallest constant $C$ that satisfies $\|P\|\hskip1pt\|Q\|\le C\|PQ\|$ for all $k$-homogeneous polynomials $P$ and $l$-homogeneous polynomials $Q$ on $E$. Our estimates are obtained using multilinear maps, the principle of local reflexivity and ideas from the geometry of Banach spaces (type and uniform convexity). We also examine the analogous problem for general polynomials on Banach spaces.

scholarly journals Trichotomy for Dynamical Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Codruţa Stoica
Keyword(s):  
Dynamical Systems ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Infinite Dimensions ◽  
Unbounded Coefficients ◽  
State Evolution

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept ofω-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples.

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