In this paper, we try to study a special class of frame wavelets in Banach spaces whose Fourier transforms are supported by frame wavelet sets. Our results generalize the various results of [2] to Banach spaces other than Hilbert spaces using the Feichtinger and Gröchenig theory. 2001 AMS Subject Classification : 42C99

We show that if f is locally in L log logL then the lacunary spherical means converge almost everywhere. The argument given here is a model case for more general results on singular maximal functions and Hilbert transforms along plane curves [6].

We extend to iP, X g p < °°, the L2 results of Bramble and Hilbert on convergence of discrete Fourier transforms and on approximation using smooth splines. The main tools are the estimates of [ 1 ] for linear functionals on Sobolev spaces and elementary results on Fourier multipliers.

We study the Gaussian Radon transform in the classical Wiener space of Brownian motion. We determine explicit formulas for transforms of Brownian functionals specified by stochastic integrals. A Fock space decomposition is also established for Gaussian measure conditioned to closed affine subspaces in Hilbert spaces.

We classify Fourier-Mukai transforms for abelian varieties. In the case of a principally polarized abelian surface these are then used to identify a large family of moduli spaces of stable vector bundles as Hilbert schemes of points on the surface.

Two independently emerging time-frequency transformations in Civil Engineering, namely, the wavelet transform and empirical mode decomposition with Hilbert transform EMD+HT , are discussed in this study. Their application to a variety of nonstationary and nonlinear signals has achieved mixed results, with some comparative studies casting significant doubt on the wavelet’s suitability for such a...

In R2, we consider an analytic family of operators Hz , z ∈ C, whose convolution kernel is obtained by taking −z − 1 derivatives of arclength measure on the parabola (t, t2) in a homogeneous way, defined in such a way so that H−1 be the standard parabolic Hilbert transform. For a fixed z, we study the set of p for which Hz is bounded on Lp(R2) and for the critical z that captures the degree of ...