pseudo-spectral theory and representations

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1: 18.38 Mathematical Applications

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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

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2: 18.39 Applications in the Physical Sciences

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Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applications^a

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Name of OP System	$w(x)$	$[a,b]$	Notation	Applications
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3: 26.19 Mathematical Applications

§26.19 Mathematical Applications

… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …

4: Wolter Groenevelt

… ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. …

5: Joris Van der Jeugt

… ►His research interests are in the following areas: Group theoretical methods in physics; Representation theory of Lie algebras, Lie superalgebras and quantum groups with applications in mathematical physics; 3$nj$-symbols and their relations to special functions and orthogonal polynomials; Quantum theory, finite quantum systems, quantum oscillator models, Wigner quantum systems; and Parabosons, parafermions and generalized quantum statistics. …

6: 13.27 Mathematical Applications

… ►Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices. …Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function. … ►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i). …

7: Donald St. P. Richards

… ►He is editor of the book Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, published by the American Mathematical Society in 1992, and coeditor of Representation Theory and Harmonic Analysis: A Conference in Honor of R. A. Kunze (with T. …

8: 27.13 Functions

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§27.13(iv) Representation by Squares

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9: Bibliography V

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Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

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§13.27.

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10: 15.17 Mathematical Applications

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§15.17(iii) Group Representations

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§15.17(v) Monodromy Groups

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