Orthogonal Similarity in Infinite- Dimensional Spaces1
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ar X iv : s ol v - in t / 9 90 90 22 v 1 2 1 Se p 19 99 SELF - SIMILARITY IN SPECTRAL PROBLEMS AND q - SPECIAL FUNCTIONS 1
Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schrödinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In particular, their algebraic structure, relations to q-special functions, infinite soliton systems, supersymmetry, coherent states, orthogonal polynomials, one...
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