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Fractional order Sobolev spaces on Wiener space
Probability Theory and Related Fields, 1993Fractional order Sobolev spaces are introduced on an abstract Wiener space and Donsker's delta functions are defined as generalized Wiener functionals belonging to Sobolev spaces with negative differentiability indices. By using these notions, the regularity in the sense of Hölder continuity of a class of conditional expectations is obtained.
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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Cosmology with the Laser Interferometer Space Antenna
Living Reviews in Relativity, 2023Germano Nardini
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An integrated space-to-ground quantum communication network over 4,600 kilometres
Nature, 2021Yu-Ao Chen, Qiang Zhang, Teng-Yun Chen
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Ab Initio Machine Learning in Chemical Compound Space
Chemical Reviews, 2021Bing Huang, O Anatole Von Lilienfeld
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Products of Wiener Functionals on an Abstract Wiener Space
1988Mikusinski in [1] has proved that the product of the distributions δ (x) and pf. \(\frac{1} {{\text{x}}}\) on the one-dimensional Euclidean space ℝ exists in the sense of generalized operations and equals \(- \frac{1} {{\text{2}}}\delta \prime \left( {\text{x}} \right)\).
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