Orthogonal polynomials and moment problem

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2004

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Topkara, Mustafa

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The generalized moment of order k of a mass distribution sigma for a natural number k is given by integral of lambda to the power k with respect to mass distribution sigma and variable lambda. In extended moment problem, given a sequence of real numbers, it is required to find a mass distribution whose generalized moment of order k is k'th term of the sequence. The conditions of existence and uniqueness of the solution obtained by Hamburger are studied in this thesis by the use of orthogonal polynomials determined by a measure on real line. A chapter on the study of asymptotic behaviour of orthogonal functions on compact subsets of complex numbers is also included.

Subject Keywords

Moment problems (Mathematics)., Orthogonal polynomials.

URI

http://etd.lib.metu.edu.tr/upload/1109164/index.pdf
https://hdl.handle.net/11511/13892

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. Topkara, “Orthogonal polynomials and moment problem,” M.S. - Master of Science, Middle East Technical University, 2004.