scholarly journals The Bezout-Corona Problem Revisited: Wiener Space Setting

2015 ◽  
Vol 10 (1) ◽  
pp. 115-139
Author(s):  
G. J. Groenewald ◽  
S. ter Horst ◽  
M. A. Kaashoek
Keyword(s):  
Wiener Space ◽  
Corona Problem ◽  
Space Setting

scholarly journals De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space

2016 ◽  
Vol 19 (02) ◽  
pp. 1650010 ◽  
Author(s):  
Nicolas Privault
Keyword(s):  
Poisson Process ◽  
Covariant Derivative ◽  
Probability Space ◽  
Differential Forms ◽  
Hodge Decomposition ◽  
Wiener Space ◽  
Harmonic Forms ◽  
Space Setting ◽  
De Rham ◽  
Poisson Space

We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham–Hodge–Kodaira decomposition as well as Weitzenböck and Clark–Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms.

scholarly journals The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 389
Author(s):  
Jeong-Gyoo Kim
Keyword(s):  
Hilbert Space ◽  
Fourier Series ◽  
Fourier Coefficients ◽  
Double Sequence ◽  
Intermediate Stage ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Abstract Space ◽  
Double Sequences ◽  
Two Parameter

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

scholarly journals Dirichlet spaces on H-convex sets in Wiener space

2011 ◽  
Vol 135 (6-7) ◽  
pp. 667-683 ◽  
Author(s):  
Masanori Hino
Keyword(s):  
Convex Sets ◽  
Wiener Space ◽  
Dirichlet Spaces

Point processes, regular variation and weak convergence

1986 ◽  
Vol 18 (01) ◽  
pp. 66-138 ◽  
Author(s):  
Sidney I. Resnick
Keyword(s):  
Weak Convergence ◽  
Function Space ◽  
Regular Variation ◽  
Point Processes ◽  
Sufficient Condition ◽  
Space Setting

A method is reviewed for proving weak convergence in a function-space setting when regular variation is a sufficient condition. Point processes and weak convergence techniques involving continuity arguments play a central role. The method is dimensionless and holds computations to a minimum. Many applications of the methods to processes derived from sums and maxima are given.

The invertibility of adapted perturbations of identity on the Wiener space

2006 ◽  
Vol 342 (9) ◽  
pp. 689-692 ◽  
Author(s):  
A. Suleyman Üstünel ◽  
Moshe Zakai
Keyword(s):  
Wiener Space

scholarly journals TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

2010 ◽  
Vol 88 (2) ◽  
pp. 205-230 ◽  
Author(s):  
CHRISTOPH KRIEGLER ◽  
CHRISTIAN LE MERDY
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unconditional Basis ◽  
Compact Set ◽  
Bounded Operators ◽  
Space Setting ◽  
Uniformly Bounded

AbstractLet K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

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