This paper formulates the moving least-square interpolation scheme in a framework of the so-called moving least-square reproducing kernel (MLSRK) representation. In this study, the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation, which, ‘as a generalization of the early discrete approach, establishes a con...

Since the development of pulse compression in the mid-1950’s the concept has become an indispensable feature of modern radar systems. A matched filter is used on reception to maximize the signal to noise ratio of the received signal. The actual waveforms that are transmitted are chosen to have an autocorrelation function with a narrow peak at zero time shift and the other values, referred to as...

Characterizing the function spaces corresponding to neural networks can provide a way understand their properties. In this paper we discuss how theory of reproducing kernel Banach be used tackle challenge. particular, prove representer theorem for wide class that admit suitable integral representation and include one hidden layer possibly infinite width. Further, show that, ReLU activation func...

We consider solving a system of semi-discrete first kind integral equations with right-hand-side being finite dimensional vector sampling values and propose regularization method for the in functional reproducing kernel Hilbert space (FRKHS), where linear functionals that define operator are continuous. A representer theorem is established, which reduces infinite problem to expresses its soluti...

Reproducing Kernel Hilbert Space (RKHS) and Reproducing Transformation Methods for Series Summation that allow analytically obtaining alternative representations for series in the finite form are developed.

Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two such ensembles have been encounted: an ensemble of unitary matrices specified by the so-called Poisson kernel, and the Laguerre ensemble of positive definite ma...