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The Cauchy problem for a linear second-order parabolic equation with 1-periodic measurable coefficients is studied in R + = {(x, t) : x ∊ Rd, t ≥ 0}, d ≥ 2. We focus at the behaviour of the fundamental solution as t → ∞. Its approximations are found with pointwise and integral error estimates of order O (t−(d+j+1)/2) and O(t−(j+1)/2), j = 0,1,…, as t → ∞, respectively. These results are applied to...
We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes...
We survey recent results in the subject of interpolating bandlimited functions from their samples at both uniform and nonuniform sets via translates of a family of multiquadrics. Recovery of the original function is considered by means of a limiting process which changes a shape parameter associated with the multiquadric function. We also discuss some ways in which approximation rates can be found...
We study the identification problem for linear time-variant communication channels on the circle, extending earlier work on the real line. We therefore resolve a suitably formulated periodic version of the conjectures of Kailath and Bello regarding channel identification.
A method is considered for determining the statistical distribution function of the field enhancement factor matrix nanoscale field emission structures from the results of emission testing. The method is based on the work of academician A.N. Tikhonov, associated with the decision of inverse ill-posed problems described by the Fredholm equation 1-st kind. In deciding it was taken into account that...
It is shown that current take-off of matrix field nanoemitters, taking into account a statistical nature of the field enhancement factor distribution of separate emitters, can be written in the form of the Fredholm equation of the first kind. A method for determination of statistical function of the field enhancement factor distribution of the matrix field emission nanostructures is proposed from...
In this paper, Walter extended the classical Shannon sampling theorem to some wavelet subspaces. We generalize the sampling theorem for multi-wavelet subspaces to multi-wavelet subspaces with a two-scaling function of Multi Resolution Analysis (MRA) based on reproducing kernel Hilbert space. Then the reconstruction function can be expressed by multi-wavelet with two scaling function of MRA using frame...
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