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On the Discrete Spectrum of Generalized Quantum Tubes
, 2005
"... The existence of discrete spectrum of the Laplacian on manifolds is an interesting phenomenon in both geometry and physics. In geometry, discrete spectrum ..."
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Cited by 9 (5 self)
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The existence of discrete spectrum of the Laplacian on manifolds is an interesting phenomenon in both geometry and physics. In geometry, discrete spectrum
The Discrete Spectrum of the Rotating Brane
, 2000
"... We elaborate on our previous suggestion that the rotating ellipsoidal membrane should have a discrete spectrum. The quasiclassical quantization is performed on the rotational modes with the result that both radii and energy are quantized. We also argue that the quantum mechanics of this system is w ..."
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We elaborate on our previous suggestion that the rotating ellipsoidal membrane should have a discrete spectrum. The quasiclassical quantization is performed on the rotational modes with the result that both radii and energy are quantized. We also argue that the quantum mechanics of this system
On the Euler characteristic of the discrete spectrum
 J. Number Theory
"... To the memory of Arnold Ross Abstract This paper, which is largely expository in nature, seeks to illustrate some of the advances that have been made on the trace formula in the past fifteen years. We review the basic theory of the trace formula, then introduce some ideas of Arthur and Kottwitz that ..."
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Cited by 6 (3 self)
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that allow one to calculate the Euler characteristic of the Scohomology of the discrete spectrum. This Euler characteristic is first expressed as a trace of a certain test function on the space of automorphic forms, and then, by the stable trace formula, is converted into a sum of orbital integrals. A
THE DISCRETE SPECTRUM FOR RADIATIVE TRANSFER WITH POLARIZATION
"... AbstractElementary consrderatrons are used to dehne and analyze the discrete spectrum for a general radratlve transfer model that Includes polarlzatmn effecls ..."
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AbstractElementary consrderatrons are used to dehne and analyze the discrete spectrum for a general radratlve transfer model that Includes polarlzatmn effecls
DISCRETE SPECTRUM OF QUANTUM TUBES
, 2006
"... A quantum tube is essentially a tubular neighborhood about an immersed complete manifold in some Euclidean space. To be more precise, let Σ ֒ → R n+k, k ≥ 1, n = dim(Σ), be an isometric immersion, where Σ is a complete, noncompact, orientable manifold. Then consider the resulting normal bundle T ⊥ Σ ..."
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spectrum. For noncompact manifolds this is in general not an easy task at all. However, using standard variational techniques, the authors Duclos, Exner, and Krejčiˇrík were able to, in an interesting paper [2], prove the existence of discrete spectra for the quantum layer (corresponding to n = 2 and
Schrödinger operators with purely discrete spectrum
, 2008
"... We prove −∆+V has purely discrete spectrum if V ≥ 0 and, for all M, {x  V (x) < M}  < ∞ and various extensions. ..."
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Cited by 3 (0 self)
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We prove −∆+V has purely discrete spectrum if V ≥ 0 and, for all M, {x  V (x) < M}  < ∞ and various extensions.
ON THE DISCRETE SPECTRUM OF COMPLEX BANDED MATRICES
, 2005
"... Abstract. The discrete spectrum of complex banded matrices that are compact perturbations of the standard banded matrix of order p is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides finiteness of the discrete spectrum is found. The pb ..."
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Cited by 1 (0 self)
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Abstract. The discrete spectrum of complex banded matrices that are compact perturbations of the standard banded matrix of order p is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides finiteness of the discrete spectrum is found. The p
Discrete spectrum for ncell potentials.
, 1998
"... We study the scattering problem, the SturmLiouville problem and the spectral problem with periodic or skewperiodic boundary conditions for the onedimensional Schrödinger equation with an ncell (finite periodic) potential. We give explicit upper and lower bounds for the distribution functions of ..."
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of discrete spectrum for these problems. For the scattering problem we give, besides, explicit upper and lower bounds for the distribution function of discrete spectrum for the case of potential consisting of n not necessarily identical cells. For the scattering problem some results about transmission
HAMILTONIANS WITH PURELY DISCRETE SPECTRUM
, 810
"... ABSTRACT. We discuss criteria for a selfadjoint operator on L 2 (X) to have empty essential spectrum. We state a general result for the case of a locally compact abelian group X and give examples for X = R n. 1. Let ∆ be the positive Laplacian on R n. We set Ba(r) = {x ∈ R n  x − a  ≤ r} and B ..."
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. Then the spectrum of the selfadjoint operator H associated to the form sum ∆ + V is purely discrete. Remark 2. Let V ± = max{±V, 0} and for each λ> 0 let Ωλ = {x  V+(x) < λ}. Then ωλ(a) is the measure of the set Ba ∩ Ωλ. From Lemma 5 it follows that the condition (i) is equivalent to dx lim
Results 1  10
of
312,563