Для функции окна двойственного к фреймам Габора предлагаются явные формулы и вычисляются константы неопределенности. Наличие явных формул позволяет усовершенствовать существующие алгоритмы разложения по таким фреймам.

Uncertainty constants for coherent states obtain irreduciable value. But problems of interpolation and orthogonalization requires the original system of functions to move to linear combinations. Localization of linear combinations of coherent states subsystems which have been set on a rectangular lattice are studied. Formulas for uncertainty constants of these combinations in general case and at additional assumptions on coefficients are received. Formulas for uncertainty constants of linear combinations of uniform shifts of Gauss function in general case and at additional assumptions on coefficients are received. Results of numerical calculations are given for the interpolating scaling functions constructed for uniform shifts of Gauss function

In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite–rank approximations by linear systems. The main result for this approach is to establish correctness of the finite–rank linear system under consideration. And the main result of the paper is to prove correctness of the finite–rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non–zero.

In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations by linear systems. The main result for this approach is to establish correctness of the finiterank linear system under consideration. And the main result of the paper is to prove correctness of the finite-rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non-zero.

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