Accession Number : ADA256448


Title :   Introduction to Real Orthogonal Polynomials


Descriptive Note : Master's thesis


Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA


Personal Author(s) : Thomas, William H , II


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a256448.pdf


Report Date : Jun 1992


Pagination or Media Count : 113


Abstract : The fundamental concept of orthogonality of mathematical objects occurs in a wide variety of physical and engineering disciplines. The theory of orthogonal functions, for example, is central to the development of Fourier series and wavelets, essential for signal processing. In particular, various families of classical orthogonal polynomials have traditionally been applied to fields such as electrostatics, numerical analysis, and many others. This thesis develops the main ideas necessary for understanding the classical theory of orthogonal polynomials. Special emphasis is given to the Jacobi polynomials and to certain important subclasses and generalizations, some recently discovered. Using the theory of hypergeometric power series and their q -extensions, various structural properties and relations between these classes are systematically investigated. Recently, these classes have found significant applications in coding theory and the study of angular momentum, and hold much promise for future applications. orthogonal polynomials, hypergeometric series.


Descriptors :   *POLYNOMIALS , *ORTHOGONALITY , SIGNAL PROCESSING , FUNCTIONS , STRUCTURAL PROPERTIES , PROCESSING , THEORY , NUMERICAL ANALYSIS , CODING , ENGINEERING , SIGNALS , POWER , ELECTROSTATICS , MOMENTUM , ANGULAR MOMENTUM , POWER SERIES , FOURIER SERIES


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE