We prove super-exponential decay estimates and holomorphic extensions for the solutions of harmonic oscillator type-equations. The functional setting for our estimates is given by the Gelfand-Shilov classes $S^{\mu}_{\nu}(\R^n),$ cf. Introduction. In the one-dimensional case, explicit solutions are given in terms of special functions of hypergeometric confluent type.

### Decay and regularity for harmonic oscillator-type equations

#### Abstract

We prove super-exponential decay estimates and holomorphic extensions for the solutions of harmonic oscillator type-equations. The functional setting for our estimates is given by the Gelfand-Shilov classes $S^{\mu}_{\nu}(\R^n),$ cf. Introduction. In the one-dimensional case, explicit solutions are given in terms of special functions of hypergeometric confluent type.
##### Scheda breve Scheda completa Scheda completa (DC)
Linear and Non-linear theory of generalized functions and its applications
Bedlewo (Polonia)
2-8 settembre 2007
20
3
283
290
Super-exponential decay; analytic estimates; Schrödinger operators; Gelfand–Shilov spaces; hypergeometric functions.
M. Cappiello; T. Gramchev; L. Rodino
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/57062