Modulation Spaces with A loc∞ -Weights

Modulation Spaces with A loc ∞ - Weights

wavelets, modulation spaces and pseudidifferential operators

مبحث تحلیل زمان-فرکانسی سیگنالها یکی از مهمترین زمینه های مورد بررسی پژوهشگران علوم ÷ایه کاربردی و فنی مهندسی میباشد.در این پایان نامه فضاهای مدولاسیون به عنوان زمینه اصلی این بررسی ها معرفی گردیده اند و نتایج جدیدی که در حوزه های مختلف ریاضی،فیزیک و مهندسی کاربرداساسی و فراوانی دارند استوار و بیان شده اند.به ویژه در این پایان نامه به بررسی و یافتن مقادیر ویژه عملگر های شبه دیفرانسیل با سمبل در...

L∞-Approximation in Korobov spaces with exponential weights

We study multivariate L∞-approximation for a weighted Korobov space of periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences a = {aj} and b = {bj} of positive real numbers bounded away from zero. We study the minimal worstcase error eL∞−app,Λ(n, s) of all algorithms that use n information evaluations fro...

Boundedness of the Riesz Projection on Spaces with Weights

Let ∂D be the unit circle in the complex plane, define the function χ on ∂D by χ(eiθ) = eiθ, and set P = {p : p = ∑Nk=−N ckχ}. Let σ be normalized Lebesgue measure on ∂D. The Riesz projection P+ is defined on P by the formula P+( ∑N k=−N ckχ k) = ∑N k=0 ckχ k. In [4], Paul Koosis proved: Theorem 1 (Koosis). Given a non-negative function w ∈ L1, there exists a non-negative, non-trivial function ...

Good Lattice Rules in Weighted Korobov Spaces with General Weights

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found. These conditions are also necessary i...