Papers by Ricardo Estrada
Journal of Physics A: Mathematical and Theoretical, 2008
In nongravitational physics the local density of energy is often regarded as merely a bookkeeping... more In nongravitational physics the local density of energy is often regarded as merely a bookkeeping device; only total energy has an experimental meaning -and it only modulo a constant term. But in general relativity the local stressenergy tensor is the source term in Einstein's equation. In closed universes, and those with Kaluza-Klein dimensions, theoretical consistency demands that quantum vacuum energy should exist and have gravitational effects, although there are no boundary materials giving rise to that energy by van der Waals interactions. In the lab there are boundaries, and in general the energy density has a nonintegrable singularity as a boundary is approached (for idealized boundary conditions). As pointed out long ago by Candelas and Deutsch, in this situation there is doubt about the viability of the semiclassical Einstein equation. Our goal is to show that the divergences in the linearized Einstein equation can be renormalized to yield a plausible approximation to the finite theory that presumably exists for realistic boundary conditions. For a scalar field with Dirichlet or Neumann boundary conditions inside a rectangular parallelepiped, we have calculated by the method of images all components of the stress tensor, for all values of the conformal coupling parameter and an exponential ultraviolet cutoff parameter. The qualitative features of contributions from various classes of closed classical paths are noted. Then the Estrada-Kanwal distributional theory of asymptotics, particularly the moment expansion, is used to show that the linearized Einstein equation with the stress-energy near a plane boundary as source converges to a consistent theory when the cutoff is removed.
Extension of Frahm formulas for δ i δ j (1/r)
Abel summability and convergence in non-tangential sectors
Ricardo Estrada and Ram P. Kanwal, Carleman type singular integral equations, SIAM Review 29 (1987), 263-290
Siam Review, 1987
Ricardo Estrada and Ram P. Kanwal, Integral equations with logarithmic kernels, IMA J.Appl.Math. 43 (1989),133-155
Ima Journal of Applied Mathematics, 1989
Distributional biharmonic equation
Distributional solutions of dual integral equations of Cauchy, Abel, and Titchmarsh types
Asymptotic Analysis: A Distributional Approach
... State University San Jose", Costa Rica University Park, PA 16802 Library of Cong... more ... State University San Jose", Costa Rica University Park, PA 16802 Library of Congress Cataloging In-Publication Data Estrada, Ricardo, 1956-Asymptotic analysis : a distributional approach /Ricardo Estrada and Ram P ... Printed and bound by Quinn-Woodbine, Woodbine, NJ. ...
Some Tauberian theorems for Schwartz distributions
Publicationes mathematicae
Distributions that are functions
Linear and Non-Linear Theory of Generalized Functions and its Applications, 2010
Abstract. It is well-known that any locally Lebesgue integrable function generates a unique distr... more Abstract. It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not ...
Expansion of distributional kernels of the type f(?x, x), as ? ? 8
Math Proc Cambridge Phil Soc, 1997
We construct an example of a series that is Abel summable but whose associated power series does ... more We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.
Aproximación asintótica de funcionales analíticos, Rev. Un. Mat. Argenentina 39 (1995), 125-136
In the present paper we obtain, from the concept of deriva- tive in the distributional sense, a s... more In the present paper we obtain, from the concept of deriva- tive in the distributional sense, a summation formula of Euler{ MacLaurin type in two variables .
Tohoku Mathematical Journal, 2012
We study Tauberian conditions for the existence of Cesàro limits in terms of the Laplace transfor... more We study Tauberian conditions for the existence of Cesàro limits in terms of the Laplace transform. We also analyze Tauberian theorems for the existence of distributional point values in terms of analytic representations. The development of these theorems is parallel to Tauber's second theorem on the converse of Abel's theorem. For Schwartz distributions, we obtain extensions of many classical Tauberians for Cesàro and Abel summability of functions and measures. We give general Tauberian conditions in order to guarantee (C, β) summability for a given order β. The results are directly applicable to series and Stieltjes integrals, and we therefore recover the classical cases and provide new Tauberians for the converse of Abel's theorem where the conclusion is Cesàro summability rather than convergence. We also apply our results to give new quick proofs of some theorems of Hardy-Littlewood and Szász for Dirichlet series. ∞ n=0 c n = γ (A) . Mathematics Subject Classification. Primary 40E05, 40G05, 40G10, 46F20; Secondary 46F10. Key words and phrases. Tauberian theorems, the converse of Abel's theorem, Hardy-Littlewood Tauberians, Szász Tauberians, distributional point values, boundary behavior of analytic functions, asymptotic behavior of generalized functions, Laplace transform, Cesàro summability.
The Cesaro behaviour of distributions
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998
The purpose of this article is to study the behaviour at infinity of generalized func-tions of on... more The purpose of this article is to study the behaviour at infinity of generalized func-tions of one real variable. The main concept explored is the Ces`aro or Riesz behaviour of distributions. It is shown that the notion of Ces`aro summability of series and inte-grals considered in ...
Distributional radius of curvature
Mathematical Methods in the Applied Sciences, 2006
We show that any continuous plane path that turns to the left has a well-defined distribution tha... more We show that any continuous plane path that turns to the left has a well-defined distribution that corresponds to the radius of curvature of smooth paths. We show that the distributional radius of curvature determines the path uniquely except for a translation. We show that Dirac ...
m-hikari.com
Several classes of entire functions of exponential type have been studied extensively [1], especi... more Several classes of entire functions of exponential type have been studied extensively [1], especially because of their importance in signal processing [11]. One of the interesting features of functions of these classes is their oscillatory properties. The aim of this article is to study some ...
Journal of Mathematical Analysis and Applications, 2003
We show that there are no continuous regularization procedures for the extension of distributions... more We show that there are no continuous regularization procedures for the extension of distributions. We also show that there are no continuous projection operators from the spaces of distributions onto subspaces of distributions with support on a given closed set.
Uploads
Papers by Ricardo Estrada