Calderón's conditions and wavelets.
The paper presents the proof of the fact that the discrete Calderón condition characterizes the completeness of an orthonormal wavelet basis.
Two remarks about spectral asymptotics of pseudodifferential operators
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.
Banach algebras of pseudodifferential operators and their almost diagonalization
We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we associate a symbol class . Then every operator with a symbol in is almost diagonal with respect to special wave packets (coherent states or Gabor frames), and the rate of almost diagonalization is described precisely by the underlying convolution algebra...
The norm of the Fourier transform on finite abelian groups
For we calculate the norm of the Fourier transform from the space on a finite abelian group to the space on the dual group.
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