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Convolutions for the Fourier transforms with geometric variables and applications
Author(s) -
Giang Bui Thi,
Mau Nguyen Van,
Tuan Nguyen Minh
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710192
Subject(s) - mathematics , sine and cosine transforms , convolution (computer science) , fourier transform , sine , convolution theorem , fourier sine and cosine series , commutative property , pure mathematics , type (biology) , algebra over a field , mathematical analysis , fourier analysis , fractional fourier transform , geometry , machine learning , artificial neural network , computer science , ecology , biology
This paper gives a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra, constructs three convolutions for the Fourier transforms with geometric variables and four generalized convolutions for the Fourier‐cosine, Fourier‐sine transforms. With respect to applications, by using the constructed convolutions normed rings on L 1 ( R n ) are constructed, and explicit solutions of integral equations of convolution type are obtained (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)