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On the Hartley – Fourier sine generalized convolution
Author(s) -
Thao Nguyen Xuan,
Van Anh Hoang Thi
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2980
Subject(s) - mathematics , convolution (computer science) , sine , factorization , convolution theorem , fourier transform , type (biology) , sine and cosine transforms , generalized function , mathematical analysis , algebra over a field , pure mathematics , fourier analysis , fractional fourier transform , algorithm , geometry , computer science , ecology , machine learning , artificial neural network , biology
In this paper, we construct and study a new generalized convolution ( f * g )( x ) of functions f , g for the Hartley ( H 1 , H 2 ) and the Fourier sine ( F s ) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities:H1 2( f * g ) ( y ) = ± (F s f ) ( y )H2 1g( y ) ,∀ y ∈ R .We prove the existence of this generalized convolution on different function spaces, such asL 1( R ) , L p α , β , γ( R ) . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd.
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