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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

Ufimsk. Mat. Zh., 2015 Volume 7, Issue 4, Pages 80–92 (Mi ufa303)

This article is cited in 5 papers

Convolution, Fourier transform and Sobolev spaces generated by non-local Ionkin problem

B. E. Kanguzhin, N. E. Tokmagambetov

Al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract: In this work, given a second order differential operator $\mathcal B$ subject to non-local boundary conditions, we assign Fourier transform and convolution to this problem. We study the properties of the introduced convolution and describe the class of test functions. We also introduce Sobolev spaces and obtain Plancherel identity related to operator $\mathcal B$.

Keywords: convolution, Fourier transform, nonlocal boundary condition, test functions, Sobolev space, Plancherel identity, differential operator, Ionkin problem.

MSC: 43A99, 46F12,42A16, 34B10, 45J05

Received: 19.02.2015


 English version:
Ufa Mathematical Journal, 2015, 7:4, 76–87

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© Steklov Math. Inst. of RAS, 2025