A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

Xuan Thao, Nguyen; Kim Tuan, Vu; Minh Khoa, Nguyen

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Some commutative neutrix convolution products of functions.

Fisher, Brian, Kiliçman, Adem (1995)

Commentationes Mathematicae Universitatis Carolinae

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Some commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1995)

Commentationes Mathematicae Universitatis Carolinae

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The commutative neutrix convolution product of the locally summable functions ${cos}_{-} (λ x)$ and ${cos}_{+} (μ x)$ is evaluated. Further similar commutative neutrix convolution products are evaluated and deduced.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

Tsankov, Yulian (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 44A35, 35L20, 35J05, 35J25 In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too. ...