Fourier Frames for Surface-Carried Measures

Oscillatory Integrals and Fourier Transforms of Surface Carried Measures

We suppose that S is a smooth hypersurface in Rn+1 with Gaussian curvature re and surface measure dS, it) is a compactly supported cut-off function, and we let pa be the surface measure with dßa = u>Ka dS. In this paper we consider the case where S is the graph of a suitably convex function, homogeneous of degree d, and estimate the Fourier transform ßa. We also show that if S is convex, with n...

Surface Measures - Maximal Functions and Fourier Transforms

On Fourier Frames

We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges’ theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a cla...

tight frame approximation for multi-frames and super-frames

در این پایان نامه یک مولد برای چند قاب یا ابر قاب تولید شده تحت عمل نمایش یکانی تصویر برای گروه های شمارش پذیر گسسته بررسی خواهد شد. مثال هایی از این قاب ها چند قاب های گابور، ابرقاب های گابور و قاب هایی برای زیرفضاهای انتقال پایاست. نشان می دهیم که مولد چند قاب تنک نرمال شده (ابرقاب) یکتا وجود دارد به طوری که مینیمم فاصله را از ان دارد. همچنین مسایل مشابه برای قاب های دوگان مطرح شده و برخی ...

Fourier Series for Singular Measures

Using the Kaczmarz algorithm, we prove that for any singular Borel probability measure μ on [0, 1), every f ∈ L2(μ) possesses a Fourier series of the form f (x) = ∑n=0 cne. We show that the coefficients cn can be computed in terms of the quantities f̂ (n) = ∫ 1 0 f (x)e −2πinxdμ(x). We also demonstrate a Shannon-type sampling theorem for functions that are in a sense μ-bandlimited.