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- W1672498982 abstract "A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applied to Jacobi operators, i.e. tridiagonal operators, on `(Z≥0), leading to a proof of Favard’s theorem stating that polynomials satisfying a three-term recurrence relation are orthogonal polynomials. We discuss the link to the moment problem. In the second example, the spectral theorem is applied to Jacobi operators on `(Z). We discuss the theorem of Masson and Repka linking the deficiency indices of a Jacobi operator on `(Z) to those of two Jacobi operators on `(Z≥0). For two examples of Jacobi operators on `(Z), namely for the Meixner, respectively Meixner-Pollaczek, functions, related to the associated Meixner, respectively Meixner-Pollaczek, polynomials, and for the second order hypergeometric q-difference operator, we calculate the spectral measure explicitly. This gives explicit (generalised) orthogonality relations for hypergeometric and basic hypergeometric series." @default.
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- W1672498982 date "2004-01-01" @default.
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- W1672498982 title "Spectral theory and special functions" @default.
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