Abstract. In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared L2 norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can...

It presents the comparison of the performance of discrete wavelets and Single-level inverse discrete 1-D wavelet transform for implementation in a still image compression system. Image compression is a method through which we can calculate the storage space of images which will helpful to calculate THR SORH, L2 norm. The performances of these transforms are compared in terms of Mean squared err...

Wavelet theory has been extensively developed in the function space L2 and discrete wavelet transform has successful applications in many areas. However, to understand better the performance of different discrete wavelet transforms, it is important to investigate their underlying discrete wavelet systems in l2. Though some preliminary results have been found recently, despite the fact that stab...

We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint e...

The Schatten norm for the nuclear operator B*?B? was estimated from both sides. Here B? : L2 ? is Berezin transform regarding Fock spaces in plane. Also, we found case of unweighted Lebesgue spaces.

In the standard scale space approach one obtains a scale space representation u : R R → R of an image f ∈ L2(R) by means of an evolution equation on the additive group (R,+). However, it is common to apply a wavelet transform (constructed via a representation U of a Lie-group G and admissible wavelet ψ) to an image which provides a detailed overview of the group structure in an image. The resul...

In this paper we devise a method for recovering band limited signals which have been subjected to a distorting procedure called companding. A band limited signal is a function in L2 whose Fourier transform vanishes outside of a bounded interval. In practice most real signals are in this class since they have no indefinitely high frequency components. The operation of companding a signal f(t) co...

The only quadrature operator of order two on L2(R) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In thi...

Consider the space L2 C, dμ z , where dμ z e−|z| 2 dz ∧ dz is the Gaussian measure, and its generalized Bargmann subspaces Em which are the null kernels of the operator Δ −∂2/∂z∂z z ∂/∂z − mI; m 0, 1, . . . . In this work, we present an other construction of Em following the Hermite functions which allows us to define a family of generalized Bargmann transform Bm which maps isometrically Em int...

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...