Fundamental solutions of the fractional Fresnel equation in the real half-line

2019 ◽  
Vol 521 ◽  
pp. 807-827 ◽  
Author(s):  
M.A. Taneco-Hernández ◽  
V.F. Morales-Delgado ◽  
J.F. Gómez-Aguilar
Keyword(s):  
Fundamental Solutions ◽  
Half Line ◽  
The Real ◽  
Fresnel Equation

scholarly journals The Wiener-Pitt Phenomenon on the Half-Line

1962 ◽  
Vol 13 (1) ◽  
pp. 37-38 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Real Line ◽  
Half Line ◽  
Stieltjes Transform ◽  
The Real

It has been well known for many years (2) that if Fμ(t) is the Fourier-Stieltjes transform of a bounded measure μ on the real line R, which is bounded away from zero, it does not follow that [Fμ(t)]−1 is also the Fourier-Stieltjes transform of a measure. It seems of interest (as was remarked, in conversation, by J. D. Weston) to consider measures on the half-line R+ = [0, ∞[, instead of on R.

scholarly journals Asymptotic Behavior of Solutions of Parabolic Equations with Unbounded Coefficients

1970 ◽  
Vol 37 ◽  
pp. 5-12 ◽  
Author(s):  
Tadashi Kuroda
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Parabolic Equations ◽  
Half Line ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Unbounded Coefficients ◽  
The Real

Let Rn be the n-dimensional Euclidean space, each point of which is denoted by its coordinate x = (x1,...,xn). The variable t is in the real half line [0, ∞).

A Singular Integral Equation with a Cauchy Kernel on the Real Half-Line

2005 ◽  
Vol 41 (12) ◽  
pp. 1775-1788 ◽  
Author(s):  
D. Pylak ◽  
R. Smarzewski ◽  
M. A. Sheshko
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Half Line ◽  
Cauchy Kernel ◽  
The Real

SQUARES OF WHITE NOISE, SL(2, ℂ) AND KUBO–MARTIN–SCHWINGER STATES

2006 ◽  
Vol 09 (04) ◽  
pp. 491-511 ◽  
Author(s):  
DMITRY V. PROKHORENKO
Keyword(s):  
White Noise ◽  
Universal Enveloping Algebra ◽  
Half Line ◽  
Probability Measures ◽  
Kms States ◽  
The Real ◽  
Enveloping Algebra ◽  
One To One

We investigate the structure of Kubo–Martin–Schwinger (KMS) states on some extension of the universal enveloping algebra of SL (2, ℂ). We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures dμ on the real half-line [0, +∞), which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.

Distribution of the smallest visited point in a greedy walk on the line

2016 ◽  
Vol 53 (3) ◽  
pp. 880-887
Author(s):  
Katja Gabrysch
Keyword(s):  
Poisson Process ◽  
Real Line ◽  
Half Line ◽  
The Real ◽  
Independence Properties

AbstractWe consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.

scholarly journals Application of Jacobi Polynomials to the Approximate Solution of a Singular Integral Equation with Cauchy Kernel on the Real Half-line

2006 ◽  
Vol 6 (3) ◽  
pp. 326-335
Author(s):  
D. Pylak
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Approximate Solutions ◽  
Half Line ◽  
Cauchy Kernel ◽  
The Real

AbstractIn this paper, exact solution of the characteristic equation with Cauchy kernel on the real half-line is presented. Next, Jacobi polynomials are used to derive approximate solutions of this equation. Moreover, estimations of errors of the approximated solutions are presented and proved.

scholarly journals ON LOOP EQUATIONS IN KdV EXACTLY SOLVABLE STRING THEORY

1992 ◽  
Vol 07 (14) ◽  
pp. 1263-1272 ◽  
Author(s):  
SIMON DALLEY
Keyword(s):  
String Theory ◽  
Cosmological Constant ◽  
The Other ◽  
Half Line ◽  
String Equation ◽  
Minimal Models ◽  
The Real ◽  
Exactly Solvable ◽  
Scale Transformations ◽  
String Theories

The non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation [Formula: see text], where [Formula: see text] generates scale transformations. In general the end of the half-line (the 'wall') is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of [P, Q]=1. Detailed arguments are given for the (2,2m-1) models while generalization to the other (p,q) minimal models and c=1 is briefly addressed.

A construction of symmetric differential expressions with non-empty essential spectrum

1987 ◽  
Vol 105 (1) ◽  
pp. 193-194 ◽  
Author(s):  
Bernd Schultze
Keyword(s):  
Essential Spectrum ◽  
Limit Point ◽  
Half Line ◽  
Simple Method ◽  
The Real ◽  
Limit Point Case

SynopsisA simple method is given for the construction of real symmetric differential expressions that are not in the limit-point case but have the real half-line as essential spectrum.

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