Results 81 to 90 of about 17,955 (266)

Uniform level set estimates for ground state eigenfunctions [PDF]

arXiv, 2017
We study the behaviour of the first eigenfunction of the Dirichlet Laplacian on a planar convex domain near its maximum. We show that the eccentricity and orientation of the superlevel sets of the eigenfunction stabilise as they approach the maximum, uniformly with respect to the eccentricity of the domain itself.
arxiv  

Characterization of Besov spaces with dominating mixed smoothness by differences

Mathematische Nachrichten, EarlyView.
Abstract Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random fields, like Gaussian fields and the stochastic heat equation, are discussed, based on a Kolmogorov ...
Paul Nikolaev, David J. Prömel, Mathias Trabs   +2 more
wiley   +1 more source

A nonlocal boundary problem for the Laplace operator in a half disk

Electronic Journal of Differential Equations, 2014
In the present work we investigate the nonlocal boundary problem for the Laplace equation in a half disk. The difference of this problem is the impossibility of direct applying of the Fourier method (separation of variables). Because the corresponding
Gani A. Besbaev, Isabek Orazov, Makhmud A. Sadybekov   +2 more
doaj  

Nodal sets of Robin and Neumann eigenfunctions [PDF]

arXiv, 2018
We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for Robin eigenfunctions in the smooth domain. For the analytic domain, the sharp upper bounds of the interior nodal sets was shown for Robin eigenfunctions. More
arxiv  

Well‐Posedness, Long‐Time Behavior, and Discretization of Some Models of Nonlinear Acoustics in Velocity–Enthalpy Formulation

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study a class of models for nonlinear acoustics, including the well‐known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamically consistent modification of the latter. Using linearization, energy estimates, and fixed‐point arguments, we establish the existence and uniqueness of solutions ...
Herbert Egger, Marvin Fritz
wiley   +1 more source

On series of Walsh eigenfunctions [PDF]

Proceedings of the American Mathematical Society, 1951
and the boundary conditions u(O) = 0, u(1) = 0, the function g(x) being assumed continuous on 0 ? x < 1. He used the asymptotic formula for the kth eigenfunction (1) uk(x) = (2)1/2 [sin k7rx + (1/k)4k(x)], | k(X) | _ C. Comparing series of these functions with corresponding series of the functions (2) Uk(X) = (2)1/2 sin kirx, he proved that if a ...
openaire   +2 more sources

Free‐Space Diffraction and Interference in a Transformed Frame

Natural Sciences, EarlyView.
In free propagation from a focus the Hermite–Gauss mode functions of optics, or the equivalent Harmonic Oscillator eigenfunctions of quantum mechanics spread in space. It is shown that a transformation to a frame travelling with the normals to the wave fronts gives the Gouy phase as proper position or time variable.
John S. Briggs
wiley   +1 more source

The Eigenfunctions of the q-Harmonic Oscillator on the Quantum Line [PDF]

arXiv, 2004
We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.
arxiv  

Multi‐Slit Diffraction in Scaled Space‐Time

Natural Sciences, EarlyView.
A space‐time scaling is used to transform quantum wave packets describing free particle motion to packets moving in an effective harmonic oscillator potential that confines and directs the wave fronts along the classical phase space of the oscillator. The transformation is applied to multi‐slit diffraction and shown to characterize diffraction features
James M. Feagin
wiley   +1 more source

Localized Eigenfunctions: Here You See Them, There You Don't [PDF]

arXiv, 2009
This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.
arxiv