Transmission eigenvalues for a class of non-compactly supported potentials
نویسندگان
چکیده
منابع مشابه
Transmission Eigenvalues for a Class of Non-Compactly Supported Potentials
Let Ω ⊆ R be a non-empty open set for which the Sobolev embedding H 0 (Ω) −→ L(Ω) is compact, and let V ∈ L∞(Ω) be a potential taking only positive real values and satisfying the asymptotics V (·) 〈·〉 for some α ∈ ]3,∞[. We establish the discreteness of the set of real transmission eigenvalues for both Schrödinger and Helmholtz scattering with these potentials.
متن کاملConstruction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix
We present a method for the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 & 0 & 1\end{array}right )$-wavelets under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an example is provided.
متن کاملResonances for Schrödinger Operators with Compactly Supported Potentials
We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactlysupported real or complex valued potential in d ≥ 1 dimensions. This note contains a sketch of the proof of our main results [5, 6] that generically the order of growth of the resonance counting function is the maximal value d in the odd dimensional case, and that it is the ma...
متن کامل1d Schrödinger Operator with Periodic plus Compactly Supported Potentials
We consider the 1D Schrödinger operator Hy = −y′′ + (p+ q)y with a periodic potential p plus compactly supported potential q on the real line. The spectrum of H consists of an absolutely continuous part plus a finite number of simple eigenvalues in each spectral gap γn 6= ∅, n > 0, where γ0 is unbounded gap. We prove the following results: 1) we determine the distribution of resonances in the d...
متن کاملMonotone and Boolean Convolutions for Non-compactly Supported Probability Measures
Abstract. The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici’s multiplicative boolean convolution it ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inverse Problems
سال: 2013
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/29/10/104006