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Characterizations of Gabor Systems via the Fourier transform.

Wojciech Czaja — 2000

Collectanea Mathematica

We give characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems. The conditions we propose are stated in terms of equations for the Fourier transforms of the Gabor system's generating functions.

Two remarks about spectral asymptotics of pseudodifferential operators

Wojciech Czaja; Ziemowit Rzeszotnik — 1999

Colloquium Mathematicae

In this paper we show an asymptotic formula for the number of eigenvalues of a pseudodifferential operator. As a corollary we obtain a generalization of the result by Shubin and Tulovskiĭ about the Weyl asymptotic formula. We also consider a version of the Weyl formula for the quasi-classical asymptotics.

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