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Patterns and structure in systems governed by linear second-order differential equations

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Abstract

This article represents a survey of transmutation ideas and their interaction with typical physical problems. For linear second-order differential operatorsP andQ one deals with canonical connectionsB:P→Q (transmutations) satisfyingQB=BP and the related transport of ‘structure’ between the theories ofP andQ. One can study in an intrinsic manner, e.g., Parseval formulas, eigenfunction expansions, integral transform, special functions, inverse problems, integral equations, and related stochastic filtering and estimation problems, etc. There are applications in virtually any area where such operators arise.

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  1. Department of Mathematics, University of Illinois at Champaign-Urbana, 273 Altgeld Hall, 1409 West Green Street, 61801, Urbana, IL, U.S.A.

    Robert Carroll

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Carroll, R. Patterns and structure in systems governed by linear second-order differential equations. Acta Appl Math 6, 109–184 (1986). https://doi.org/10.1007/BF00046724

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