Electron. J. Diff. Eqns., Vol. 2002(2002), No. 64, pp. 125.
Expansions of solutions of higher order evolution
equations in series of generalized heat polynomials
G. N. Hile & Alexander Stanoyevitch
Abstract:
Upper bound estimates are established on generalized heat
polynomials for higher order linear homogeneous evolution
equations with coefficients depending on the time variable.
These estimates are analogous to well known bounds of Rosenbloom
and Widder on the heat polynomials. The bounds lead to further
estimates on the width of the strip of convergence of series
expansions in terms of these polynomial solutions. An application
is given to a Cauchy problem, wherein the solution is expressed
as the sum of a series of polynomial solutions.
Submitted January 22, 2002. Published July 11, 2002.
Math Subject Classifications: 35C10, 35K25, 35C05, 35K30.
Key Words: heat polynomials, polynomial solutions,
evolution equations, series expansions.
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Gerald N. Hile
Department of Mathematics
University of Hawaii
Honolulu, HI 96822, USA
email: hile@hawaii.edu 

Alexander Stanoyevitch
Department of Mathematics
University of Guam
UOG Station, Mangilao, GU 96923, USA
email: alex@math.hawaii.edu 
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