Recurrence relations for radial positive definite functions
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In the theory of radial basis functions as well as in the theory of spherically symmetric characteristic functions, recurrence relations are used to construct \(d\)-dimensional functions starting with lower-dimensional ones. The author shows that the operators used so far are special cases of one-step recurrence relations for \(\ell_2\)-radial positive definite functions. He further gives the analogue for \(\ell_1\)-radial functions and thereby defines a turning bands operator for 1-symmetric characteristic functions.
Meijer's G-function, recurrence relations, radial positive definite functions, Applied Mathematics, Positive definite functions in one variable harmonic analysis, Spherically symmetric characteristic functions, Turning bands operator, Radial basis functions, Fractional operators, Applications of hypergeometric functions, Fractional derivatives and integrals, turning bands operator, Positive definite functions on groups, semigroups, etc., spherically symmetric characteristic functions, Analysis
Meijer's G-function, recurrence relations, radial positive definite functions, Applied Mathematics, Positive definite functions in one variable harmonic analysis, Spherically symmetric characteristic functions, Turning bands operator, Radial basis functions, Fractional operators, Applications of hypergeometric functions, Fractional derivatives and integrals, turning bands operator, Positive definite functions on groups, semigroups, etc., spherically symmetric characteristic functions, Analysis
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