A Generalization of Gordon ' S Theorem Andapplications to Quasiperiodic Schr
نویسنده
چکیده
We prove a criterion for absence of eigenvalues for one-dimensional Schrr odinger operators. This criterion can be regarded as an L 1-version of Gor-don's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, HH older continuous functions and functions with power-type singularities. The proof is based on Gronwall-type a priori estimates for solutions of Schrr odinger equations.
منابع مشابه
GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM
In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.
متن کاملA generalization of Martindale's theorem to $(alpha, beta)-$homomorphism
Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.
متن کاملA Generalization of Gordon’s Theorem and Applications to Quasiperiodic Schrödinger Operators
We present a criterion for absence of eigenvalues for one-dimensional Schrödinger operators. This criterion can be regarded as an L1-version of Gordon’s theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, Hölder continuous functions and...
متن کاملGeneralization of Darbo's fixed point theorem and application
In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.
متن کاملA new characterization for Meir-Keeler condensing operators and its applications
Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...
متن کامل