Progressive Gelfand-Shilov Spaces and Wavelet Transforms
نویسندگان
چکیده
منابع مشابه
Wavelet transforms on Gelfand-Shilov spaces and concrete examples
In this paper, we study the continuity properties of wavelet transforms in the Gelfand-Shilov spaces with the use of a vanishing moment condition. Moreover, we also compute the Fourier transforms and the wavelet transforms of concrete functions in the Gelfand-Shilov spaces.
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In this paper the wavelet transformation on Gelfand and Shilov spaces of type WM ( ), W (∆) and W M (∆ ) is studied. It is shown that Wψφ :WM ( )→WM ( n × +), Wψφ :W Ω (∆)→W (∆ × +) andWψφ :W M (∆)→W M (∆ × +) is linear and continuous where n and ∆ are n-dimensional real numbers and complex numbers. A boundedness result in a generalized Sobolev space is derived.
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The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces S, where 0 < β < 1 . This result leads to a refinement of previous generalizations of the loca...
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The Cauchy problem for systems of differential equations with multiplicative random perturbations in the form of infinitedimensional Ito integrals is studied. For the systems correct by Petrovskii, conditionally correct and incorrect we point out Gelfand–Shilov spaces of generalized functions where a generalized solution coincides with a mild solution. AMS Mathematics Subject Classification (20...
متن کاملWavelet Transforms in Generalized Fock Spaces
ABSTP,CT. A generalized Fock space is introduced as it was developed by Schmeelk [1-5], also Schmeelk and Takai [6-8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by Mikusinski and Mort [9] based upon earl...
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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2012
ISSN: 0972-6802,1758-4965
DOI: 10.1155/2012/951819