Results 101 to 110 of about 7,103 (240)

An Observation on Eigenfunctions of the Laplacian

La Matematica
In his seminal 1943 paper F. Rellich proved that, in the complement of a cavity $Ω= \{x\in \mathbb R^n\mid |x|>R_0\}$, there exist no nontrivial solution $f$ of the Helmholtz equation $Δf = - λf$, when $λ>0$, such that $\int_Ω |f|^2 dx < \infty$.
Banerjee, Agnid, Garofalo, Nicola
openaire   +3 more sources

On the localization Eigenfunction expansions associated with the Schrodinger Operator

, 2013
In this paper we study eigenfunction expansions associated with the Schrodinger operator with a singular potential. In the paper it is obtained sufficient conditions for localization and uniformly convergence of the regularizations of the corresponding
Rakhimov, Abdumalik
core   +1 more source

Optimal Recovery of Rayleigh‐Wave Overtones by Multi‐Directional Acquisition

Geophysical Research Letters
Rayleigh waves are ubiquitously used for subsurface characterization through dispersion curve inversion, whose quality depends on the number of useable overtones.
A. Lellouch, E. Shimony, P. Sinitsyn
doaj   +1 more source

On the eigenfunction expansions associated with the Schrodinger operator

, 2012
The paper devoted to investigation of the behavior near the boundary of eigenfunction expansions associated with Schrodinger ...
Rakhimov, Abdumalik A.
core  

On the behaviour of eigenfunction expansions in the complex domain

, 1986
SynopsisBy using asymptotic estimates for the eigenvalues and eigenfunctions or irregular boundary value problems, we state necessary conditions for the pointwise convergence and for the divergence of the corresponding eigenfunction expansions.
Gerhard Freiling
core   +1 more source

Boundary value problems for essentially-loaded parabolic equation

Қарағанды университетінің хабаршысы. Математика сериясы, 2018
In this paper we investigate the first boundary value problem for essentially loaded equation of heat conduction, i.e. when laden terms are derivatives for any finite order.
M.I. Ramazanov, M.T. Kosmakova, V.G. Romanovsky, B.H. Zhanbusinova, Zh.M Tuleutaeva   +4 more
doaj   +1 more source

A counter-example to log-concavity of the first Robin eigenfunction

, 2017
The first Neumann eigenfunction is a constant, while the first Dirichlet eigenfunction is known to be log-concave, by a result of Brascamp and Lieb.
Clutterbuck, Julie
core  

Note on a non standard eigenfunction of the planar Fourier transform

, 2017
The aim of this note is to consider a non trivial example of distributional eigenfunction of the planar Fourier transform. This eigenfunction is not a tensor product of univariate eigenfunctions.
V. Maz’ya, Maz'ya, Vladimir, F. Lanzara, LANZARA, Flavia   +3 more
core   +1 more source

Exponential decay of two-body eigenfunctions: A review

Electronic Journal of Differential Equations, 2000
We review various results on the exponential decay of the eigenfunctions of two-body Schrödinger operators. The exponential, isotropic bound results of Slaggie and Wichmann for eigenfunctions of Schrödinger operators corresponding to eigenvalues below ...
Peter Hislop
doaj  

Numerical solution of the multi-order fractional differential equation using Legendre wavelets and eigenfunction approach

Partial Differential Equations in Applied Mathematics
An eigenfunction approach is implemented in this article to solve the multi-order fractional differential equations (FDEs) with boundary conditions. The approximate unknown solution is expressed as a linear combination of eigenfunctions in the present ...
Shivani Ranta, Sandipan Gupta, Dileep Kumar Sharma   +2 more
doaj   +1 more source