Related papers: On regularizations of the integral representation …
The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative…
We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory…
The problem of calculating the Mittag-Leffler function $E_{\rho,\mu} (z)$ is considered in the paper. To solve this problem integral representations for the function $E_{\rho,\mu}(z)$ are transformed in such a way that they could not…
We study the evolution equations for a regularized version of Dirac-geodesics, which are the one-dimensional version of Dirac-harmonic maps. We show that for the regularization being sufficiently large, the evolution equations subconverge…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
Using Cauchy's Integral Theorem as a basis, what may be a new series representation for Dirichlet's function $\eta(s)$, and hence Riemann's function $\zeta(s)$, is obtained in terms of the Exponential Integral function $E_{s}(i\kappa)$ of…
The Dirac's bra-ket formalism is generalized to finite-dimensional vector spaces with indefinite metric in a simple mathematical context similar to thatof the theory of general tensors where, in addition, scalar products are introduced with…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
We perform the Dirac quantization of RS fields interacting with a spinor and the first derivative of a pseudoscalar field. We achieve the calculations for two forms of this interaction: first we review the conventional coupling of lowest…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for…
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…