On the Riesz constants for systems of integer translates

Periodic wavelet frames and time–frequency localization

“…Finally, substituting (12), (13), and (15) in Definition 2 and calculating the limit we obtain lim a→∞ U C(η a,0 j ) = Proof of Theorem 4. 1.…”

“…The case of wavelet basis is an open problem and it is a task for future work. In this direction, some useful properties of shifted Gaussian are discussed in [13]. We will consider the particular issue of wavelet sequences in Section 4.…”

О Константах Рисса Для Некоторых Систем Целочисленных Сдвигов

“…Выразить через известные специальные функции коэф-фициенты разложения узловой функции и саму узловую функцию для системы сдвигов функции Лоренца. Некоторые результаты получены в [55]- [56].…”

“…Problem 2. Prove symmetry and sign changing for coefficients in (5), some results are proved in [26], [55]- [56].…”

On the Correctness of Finite-Rank Approximations by Series of Shifted Gaussians

“…In [1] the solution is derived with using special functions, exactly Jacobi theta-functions. But as it was demonstrated in [2]- [3] in spite of theoretical value such approach has not computational perspectives as it involves division on very small denominators which leads to large numerical errors. Another approach based on discreet Fourier transform (DFT) is effective but for very small range of parameters [3].…”