Vol. 69, No. 2, pp. 133–143 (2017)

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On generalizations of Boehmian space and Hartley transform

C. Ganesan and R. Roopkumar

C.G.: Department of Mathematics, V. H. N. S. N. College, Virudhunagar - 626001, India. E-mail: c.ganesan28@yahoo.com and R.R.:Department of Mathematics, Central University of Tamil Nadu, Thiruvarur - 610101, India. E-mail: roopkumarr@rediffmail.com

Abstract: Boehmians are quotients of sequences which are constructed by using a set of axioms. In particular, one of these axioms states that the set S from which the denominator sequences are formed should be a commutative semigroup with respect to a binary operation. In this paper, we introduce a generalization of abstract Boehmian space, called generalized Boehmian space or G-Boehmian space, in which S is not necessarily a commutative semigroup. Next, we provide an example of a G-Boehmian space and we discuss an extension of the Hartley transform on it.

Keywords: Bohemians; convolution; Hartley transform.

Classification (MSC2000): 44A15; 44A35, 44A40

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Electronic fulltext finalized on: 24 Feb 2017. This page was last modified: 17 Mar 2017.

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