共查询到20条相似文献,搜索用时 78 毫秒
1.
Masayoshi Takeda 《Journal of Functional Analysis》2002,191(2):343-376
We obtain a necessary and sufficient condition for conditional gaugeability and show the equivalence between conditional gaugeability and subcriticality of generalized Schrödinger type operators. We apply the condition to concrete examples. 相似文献
2.
Zhen-Qing Chen 《Journal of Functional Analysis》2003,202(1):226-246
An analytic characterization of gaugeability and conditional gaugeability is given for non-local (or discontinuous) Feynman-Kac transforms of general symmetric Markov processes. This analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases. 相似文献
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Franç ois Germinet Abel Klein 《Proceedings of the American Mathematical Society》2003,131(3):911-920
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
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Jean-Marc Bouclet Franç ois Germinet Abel Klein 《Proceedings of the American Mathematical Society》2004,132(9):2703-2712
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators. We prove sub-exponential decay for functions in Gevrey classes and exponential decay for real analytic functions.
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The relation between Hausdorff dimension of the singular spectrum of a Schrödinger operator and the decay of its potential has been extensively studied in many papers. In this work, we address similar questions from a different point of view. Our approach relies on the study of the so-called Krein systems. For Schrödinger operators, we show that some bounds on the singular spectrum, obtained recently by Remling and Christ-Kiselev, are optimal.
7.
David Damanik Dirk Hundertmark 《Proceedings of the American Mathematical Society》2004,132(7):1957-1962
We prove a criterion for absence of decaying solutions for one-dimensional Schrödinger operators. As necessary input, we require infinitely many centers of local reflection symmetry and upper and lower bounds for the traces of the associated transfer matrices.
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S. Northshield 《随机分析与应用》2013,31(4):461-482
In this paper we study certain edge-weighted random walks on infinite graphs with bounded vertex degree for which the second smallest eigenvalue of the Laplacian is negative.We find analogues of the Feynman-Kac functional and give several conditions equivalent to the boundeness of the corresponding gauge function.From this result we derive a new formula for the second smallest eigenvalue of the Laplacian and we apply this formula to the theory of graph coverings.An analogue of the conditional gauge theorem is shown to hold for certain Schrödinger operators. 相似文献
10.
Pourhadi Ehsan Khrennikov Andrei Yu. Oleschko Klaudia de Jesús Correa Lopez María 《Journal of Fourier Analysis and Applications》2020,26(4):1-12
We consider the pointwise convergence problem for the solution of Schrödinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson’s problem as the simplest case and was studied in general by Cho et al. We extend their result from the case of the classical Schrödinger equation to a class of equations which includes the fractional Schrödinger equations. To achieve this, we significantly simplify their proof by completely avoiding a time localization argument. 相似文献
11.
New unique characterization results for the potential in connection with Schrödinger operators on and on the half-line are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schrödinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schrödinger operators with confining potentials on the entire real line.
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Mikló s Horvá th Má rton Kiss 《Proceedings of the American Mathematical Society》2006,134(5):1425-1434
For Schrödinger operators with nonnegative single-well potentials ratios of eigenvalues are extremal only in the case of zero potential. To prove this, we investigate some monotonicity properties of Prüfer-type variables.
13.
Christian Remling 《Proceedings of the American Mathematical Society》2007,135(10):3329-3340
We point out finite propagation speed phenomena for discrete and continuous Schrödinger operators and discuss various types of kernel estimates from this point of view.
14.
Kasso A. Okoudjou Robert S. Strichartz 《Proceedings of the American Mathematical Society》2007,135(8):2453-2459
In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpinski gasket . In particular, using the existence of localized eigenfunctions for the Laplacian on we show that the eigenvalues of the Schrödinger operator break into clusters around certain eigenvalues of the Laplacian. Moreover, we prove that the characteristic measure of these clusters converges to a measure. Results similar to ours were first observed by A. Weinstein and V. Guillemin for Schrödinger operators on compact Riemannian manifolds.
15.
Alexander Pankov 《Proceedings of the American Mathematical Society》2008,136(7):2565-2570
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schrödinger equations. Under certain natural assumptions we show that any such solution is continuous and vanishes at infinity. This allows us to interpret the solution as a finite multiplicity eigenfunction of a certain linear Schrödinger operator and, hence, apply well-known results on the decay of eigenfunctions.
16.
M. Cobo C. Gutierrez C. R. de Oliveira 《Proceedings of the American Mathematical Society》2008,136(3):923-930
It is shown that Schrödinger operators, with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, have Cantor spectrum of measure zero and pure singular continuous for Lebesgue almost all points of the interval.
17.
Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L 2 -infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form. 相似文献
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David Damanik Michael Landrigan 《Proceedings of the American Mathematical Society》2003,131(7):2209-2216
We consider discrete one-dimensional Schrödinger operators on the whole line and establish a criterion for continuity of spectral measures with respect to log-Hausdorff measures. We apply this result to operators with Sturmian potentials and thereby prove logarithmic quantum dynamical lower bounds for all coupling constants and almost all rotation numbers, uniformly in the phase.
19.
In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to study the surjectivity of magnetic Schrödinger operators on bundles over graphs. 相似文献
20.
Hongjie Dong Wolfgang Staubach 《Proceedings of the American Mathematical Society》2007,135(7):2141-2149
We obtain unique continuation results for Schrödinger equations with time dependent gradient vector potentials. This result with an appropriate modification also yields unique continuation properties for solutions of certain nonlinear Schrödinger equations.