Heat “polynomials” for a singular differential operator on (0,\(\infty)\). (English) Zbl 0696.41027

Summary: We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operators on (0,\(\infty)\). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials in x and t, however, this property does not hold in general.


41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
41A10 Approximation by polynomials
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
35K05 Heat equation
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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