On Gevrais classes of certain self-adjoint differential operators with degeneration
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Classical spaces of ultradifferentiable functions on [−1,1] are compared with the Gevrais classes of a self-adjoint differential operator whose eigenfunctions are orthogonal Jacobi polynomials.
KeywordsDifferential Operator Jacobi Polynomial Classical Space Ultradifferentiable Function Orthogonal Jacobi Polynomial
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- 1.V. L. Gorbachuk, “On the summability of expansions in eigenfunctions of self-adjoint operators,”Dokl. Akad. Nauk SSSR,292, No. 1, 20–25 (1987).Google Scholar
- 2.E. V. Martynenko, “Self-adjoint boundary-value problems for a differential equation with degeneration,” in:Boundary-Value Problems for Differential Operator Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991), pp. 63–69.Google Scholar
- 3.H. Bateman and A. Erdélyi,Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1953).Google Scholar
- 4.P. K. Suetin,Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1976).Google Scholar
- 5.V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, and A. F. Turbin,A Handbook of Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1985).Google Scholar