Abstract
Boehmians are used for all objects obtained by an algebraic construction similar to that of the field of quotients. In literature, several integral transforms have been extended to various Boehmian spaces but a few to the space of strong Boehmians. As shown in the work of Al-Omari (2013), this work describes certain spaces of Boehmians. The Sumudu transform is therefore established and it is one-one and continuous in the space of Boehmians. The inverse transform is given and some results are also discussed.
Highlights
Integral transforms are widely used in the literature, where some are often used for solving differential equations
Sumudu transform was introduced by Watugala [1] and discussed by Weerakoon in [2]
Sumudu transform has been investigated over functions of two variables
Summary
Integral transforms are widely used in the literature, where some are often used for solving differential equations. Having scale and unit-preserving properties, the Sumudu transform can be used to solve problems without resorting to new frequency domains. In [7] the classical theorems in [6] are extended to distribution spaces and a space of Boehmians. In this note we discuss the cited transform on certain space of strong Boehmians. The general construction of usual and strong Boehmians is given in Sections 2 and 3, respectively. The Sumudu transform of f(x) is given by [1]. The Sumudu transform of the convolution product is given as μ (f ⊛ g) (ζ) = ζf(ζ) g (ζ) ,. Following are general properties of Sumudu transforms. For usual Boehmians, see [10,11,12,13,14,15,16,17,18,19]
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