Related papers: Fourier transforms of positive definite kernels an…
The first part I talk about the motivation for Lu Qi-Keng conjecture and the results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in ${\bf{C^n}}$. The second part I summarize the main results on…
Let $V$ be a finite dimensional real vector space. In the article we construct an isomorphism between the space of smooth translation invariant valuations on convex subsets of $V$ and the space of such valuations (twisted by densities) on…
Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we…
We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
Diffraction of coherent x-ray beams is treated through the Fractionnal Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modulo gauge transformations. Since this space is a compact…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…
We find an interpretation of the recent finding that the central charge density of the neutron is negative by using models of generalized parton distributions at zero skewness to relate the behavior of deep inelastic scattering quark…
In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…
Positive definite functions are very important in both theory and applications of approximation theory, probability and statistics. In particular, identifying strictly positive definite kernels is of great interest as interpolation problems…
The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied,…
We offer further results on a general size-biased distribution related to the Riemann xi-function we presented in [9] using the work of Ferrar. Curious properties associated with its expected value are presented, which are related to…