Gelfand-Shilov spaces for the Hankel transform

2 Redefinition of the presheaf of Gelfand - Shilov spaces

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...

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.

THE n-DIMENSIONAL CONTINUOUS WAVELET TRANSFORMATION ON GELFAND AND SHILOV TYPE SPACES

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.

Generalized Solutions to Stochastic Systems with Multiplicative Noise in Gelfand–shilov Spaces

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...

The Hankel transform