Results 131 to 140 of about 112,078 (333)

Reconstructing potentials from zeros of one eigenfunction

, 2011
. We study an inverse nodal problem, concerning the reconstruction of a potential of a Sturm-Liouville operator, by using zeros of one eigenfunction as input.
Xinfu Chen, And Y. H. CHENG, C. Law
semanticscholar   +1 more source

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

On the geometric structures of transmission eigenfunctions with a conductive boundary condition and applications [PDF]

arXiv, 2018
This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [9]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less
arxiv  

Eigenfunction Expansions Associated with Second-order Differential Equations for Hilbert Space-valued Functions

, 1971
where for each r € HO, oo) A(r) is an operator in a Hilbert space H and & acts on ^-valued functions on fO, co). Restricting the domain of
Yoshimi Saito
semanticscholar   +1 more source

Nonparametric identification of positive eigenfunctions [PDF]

Econometric Theory, 2014
Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk–return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models.
openaire   +5 more sources

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

Graph Eigenfunctions and Quantum Unique Ergodicity [PDF]

arXiv, 2010
We apply the techniques of our previous paper to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of $\mathbb{H}\times\mathbb{H}$.
arxiv  

Long Term Risk: An Operator Approach [PDF]

We create an analytical structure that reveals the long run risk-return relationship for nonlinear continuous time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family ...
Jose Scheinkman, Lars Peter Hansen
core  

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   +2 more sources

Doubling property and vanishing order of Steklov eigenfunctions [PDF]

arXiv, 2014
The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunction on the boundary of a smooth boundary domain $\mathbb R^n$. The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling property shown by Lin and Bellova \cite{BL}.
arxiv