CUBO A Mathematical Journal Vol.12, N° 03, (203–212). October 2010

Analytic Continuation and Applications of Eigenvalues of Daubechies’ Localization Operator

KUNIO YOSHINO

Department of Natural Sciences, Faculty of Knowledge Engineering, Tokyo City University, Tokyo 158-8557, Japan email: yoshinok@tcu.ac.jp

ABSTRACT

In this paper we introduce generating functions of eigenvalues of Daubechies’ localization operator, study their analytic properties and give analytic continuation of these eigenvalues. Making use of generating functions, we establish a reconstruction formula of symbol functions of Daubechies’ localization operator with rotational invariant symbols.

Key words and phrases: Hermite functions, Daubechies (localization) operator, Borel transform, asymptotic expansion.

RESUMEN

Introducimos funciones generadas por los autovalores del operador de localización de Daubechies, estudiamos sus propiedades analíticas y damos continuación analítica de los autovalores. Haciendo uso de las funciones generadas, establecemos la fórmula de reconstrucción de funciones símbolo del operador de localización de Daubechies con símbolos rotacional invariante.

Math. Subj. Class.: 33, 44, 46F.

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