Lobachevsky-type formulas via Fourier analysis
Copyright policy )Lobachevsky-type formulas via Fourier analysis
Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving the cardinal sine motivate an extension of the classical Parseval formula involving both periodic and non-periodic functions. We develop a version of the Parseval formula that is often more practical in applications and illustrate its use by extending recent results on Lobachevsky-type integrals. Some previously known, interesting identities are re-proved in a more transparent manner and new formulas for integrals involving cardinal sine and Bessel functions are given.
8 pages
- Shanghai Jiao Tong University China (People's Republic of)
Signal theory (characterization, reconstruction, filtering, etc.), Shannon basis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Functions of bounded variation, generalizations, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Lobachevsky-type integral
Signal theory (characterization, reconstruction, filtering, etc.), Shannon basis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Functions of bounded variation, generalizations, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Lobachevsky-type integral
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