Boehmians of type S and their Fourier transforms
نویسندگان
چکیده
Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
منابع مشابه
Integrable Boehmians, Fourier Transforms, and Poisson’s Summation Formula
Boehmians are classes of generalized functions whose construction is algebraic. The first construction appeared in a paper that was published in 1981 [6]. In [8], P. Mikusiński constructs a space of Boehmians, βL1(R), in which each element has a Fourier transform. Mikusiński shows that the Fourier transform of a Boehmian satisfies some basic properties, and he also proves an inversion theorem. ...
متن کاملA Brief Investigation of a Stieltjes Transform in a Class of Boehmians
Various integral transforms have been extended to various spaces of Boehmians. In this article, we discuss the Stieltjes transform in a class of Boehmians. The presented transform preserves many properties of the classical transform in the space of Boehmians.
متن کاملWavelet Analysis on a Boehmian Space
We extend the wavelet transform to the space of periodic Boehmians and discuss some of its properties. 1. Introduction. The concept of Boehmians was introduced by J. Mikusi´nski and P. Mikusi´nski [7], and the space of Boehmians with two notions of conver-gences was well established in [8]. Many integral transforms have been extended to the context of Boehmian spaces, for example, Fourier trans...
متن کاملMeasurement of Plain Weave Fabrics Density Using Fourier Transforms
Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...
متن کاملMeasurement of Plain Weave Fabrics Density Using Fourier Transforms
Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...
متن کامل