scholarly journals Rotations and Tangent Processes on Wiener Space

2004 ◽  
pp. 205-225 ◽  
Author(s):  
Moshe Zakai
Keyword(s):  
Wiener Space

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

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 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 Some covariance inequalities in Wiener space

2008 ◽  
Vol 255 (9) ◽  
pp. 2563-2578
Author(s):  
E. Mayer-Wolf ◽  
A.S. Üstünel ◽  
M. Zakai
Keyword(s):  
Wiener Space

Dirichlet Forms and Analysis on Wiener Space

1993 ◽  
Vol 25 (2) ◽  
pp. 206-207
Author(s):  
J. R. Norris
Keyword(s):  
Dirichlet Forms ◽  
Wiener Space
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