For appropriate orthonormal wavelet basis {ψjke}j∈Zk∈Zde∈{0,1}d, constants p and γ, if Iγdenotes the Riesz fractional integral operator of order γ and (ηjke)j∈Zk∈Zde∈{0,1}d a sequence of independent identically distributed symmetric p-stable random variables, we investigate the convergence of the series ΣjkeηjkeIγψjke. Similar results are also studied for modified fractional integral operators. Finally, some geometric properties related to self similarity are studied.

Some general conditions for multichannel sampling are established for wide sense stationary sequences with spectral density. First, necessary and sufficient conditions are given for these processes so that they are linearly determined by the samples obtained from a multichannel sampling scheme. Some results are studied for stationary sequences and then applied to the problem of sampling, not necessarily band limited, wide sense stationary processes. Conditions are also given for the existence of a frame sequence of the samples. In the case of frames, the condition that the spectral measure is absolutely continuous is proved to be necessary.

We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.

In this paper, we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns the representation of continuous time wide sense stationary random processes by means of discrete samples.

In this paper we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns to the possible representation of continuous time processes by means of discrete samples.

This paper studies the almost sure almost every where convergence of random series of the form Sigmai=1infinaifiLebesgue spaces LP(X, Sigma, mu), where the ai's are centered random variables, and the fi's constitute an unconditional basic sequence.

We provide an almost-sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and rather simple probability theory results.

We construct an a.s. convergent expansion of a /spl prop/1/|/spl omega/|/sup /spl beta// spectral behavior process.