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The Algebraic Multiplicity of Eigenvalues and the Evans Function Revisited

Y. Latushkin, A. Sukhtayev (2010)

Mathematical Modelling of Natural Phenomena

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pencil. In the second part of the paper we apply this result...

The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms.

Lenz, Daniel, Stollmann, Peter, Veselić, Ivan (2009)

Documenta Mathematica

The Calderón Projector for an Elliptic Operator in Divergence Form.

Marcela Sanmartino (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

The Cauchy-Riemann operator in infinite dimensional spaces.

Roberto Luiz Soraggi (1990)

Revista Matemática de la Universidad Complutense de Madrid

The characterization of differential operators by locality : classical flows

Ola Bratteli, George A. Elliott, Derek W. Robinson (1986)

Compositio Mathematica

The cokernel of the operator $\partial / \partial x_{n}$ acting on a $𝒟_{n}$ -module, II

Arno Van den Essen (1985)

Compositio Mathematica

The density of states of a local almost periodic operator in $ℝ^{ν}$

Andrzej Krupa (2003)

Studia Mathematica

We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on $H^{m} (ℝ^{ν})$ . The support of the density coincides with the spectrum of the operator in $L ² (ℝ^{ν})$ .

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya, Igor Verbitsky (2004)

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $ℝ^{n}$ for the relativistic Schrödinger operator $\sqrt{- Δ} + Q$ to be bounded as an operator from the Sobolev space $W_{2}^{1 / 2} (ℝ^{n})$ to its dual $W_{2}^{- 1 / 2} (ℝ^{n})$ .

The initial value problem for parabolic equations with data in $L^{p} (R^{n})$

Eugene Fabes (1972)

Studia Mathematica

The integral equation methods for the perturbed Helmholtz eigenvalue problems.

Khelifi, Abdessatar (2005)

International Journal of Mathematics and Mathematical Sciences

The laplacian and the Dirac operator in infinitely many variables

R. J. Plymen (1980)

Compositio Mathematica

The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces

Roman Lávička (1998)

Commentationes Mathematicae Universitatis Carolinae

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

The low energy expansion in nonrelativistic scattering theory

S. Albeverio, F. Gesztesy, R. Høegh-Krohn (1982)

Annales de l'I.H.P. Physique théorique

The norm estimate of the difference between the Kac operator and Schrödinger semigroup. II: The general case including the relativistic case.

Ichinose, Takashi, Takanobu, Satoshi (2000)

Electronic Journal of Probability [electronic only]

The Role of Green’s Functions in Inverse Scattering at Fixed Energy

James Ralston (1996/1997)

Séminaire Équations aux dérivées partielles

The short-range expansion in solid state physics

Helge Holden, Raphael Høegh-Krohn, Steinar Johannesen (1984)

Annales de l'I.H.P. Physique théorique

The Sobolev-Il'in theorem for the $B$ -Riesz potential.

Guliev, V.S., Garakhanova, N.N. (2009)

Sibirskij Matematicheskij Zhurnal

The solution of the Kato problem in two dimensions.

Steve Hofmann, Alan McIntosh (2002)

Publicacions Matemàtiques

We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L12(R2) → L2(R2).[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential.

M.M. Skriganov (1985)

Inventiones mathematicae

The spectrum of Schrödinger operators with random $δ$ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

We shall consider the Schrödinger operators on $ℝ^{2}$ with the magnetic field given by a nonnegative constant field plus random $δ$ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

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