The following propositions hold:. A classical reference on convergence is [Wa]. Some generalizations can be found in [Br] , [Sk] , [Bo].
Orthogonal Functions: Moment Theory and Continued Fractions
Moment problem ; orthogonal polynomials ; number theory ; and the metrical theory of continued fractions see also Metric theory of numbers. Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. Around J.
Comments A classical reference on convergence is [Wa]. References [Bo] D. A type of continued fraction, referred to as a J-fraction, is shown to correspond to a power series about the origin and to another power series about infinity such that the successive convergents of this fraction include two more additional terms of anyone of the power series.
Given the power series expansions, a method of obtaining such a J-fraction, whenever it exists, is also looked at. The first complete proof of the so called strong Hamburger moment problem using a continued fraction is given.
In this case the continued fraction is a J-fraction. Finally a special class of J-fraction, referred to as positive definite J-fractions, is studied in detail.
Communications in the Analytic Theory of Continued Fractions (CATCF) | Colorado Mesa Univ.
The four chapters of this thesis are divided into sections. Each section is given a section number which is made up of the chapter number followed by the number of the section within the chapter. The equations in the thesis have an equation number consisting of the section number followed by the number of the equation within that section. In Chapter One, in addition to looking at some of the historical and recent developments of corresponding continued fractions and their applications, we also present some preliminaries.
Chapter Two deals with a different approach of understanding the properties of the numerators and denominators of corresponding two point rational functions and, continued fractions.
This approach, which is based on a pseudo orthogonality relation of the denominator polynomials of the corresponding rational functions, provides an insight into understanding the moment problems. In particular, results are established which suggest a possible type of continued fraction for solving the strong Hamburger moment problem. William B.
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