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Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

Demontis, Francesco, der Mee, Cornelis van (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.

Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces

Nils Reich (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

For a class of anisotropic integrodifferential operators arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations u = f on [0,1]n with possibly large n. Under certain conditions on , the scheme is of essentially optimal and dimension independent complexity 𝒪 (h-1| log h |2(n-1)) without corrupting the convergence or smoothness requirements...

Weak almost periodicity of L 1 contractions and coboundaries of non-singular transformations

Isaac Kornfeld, Michael Lin (2000)

Studia Mathematica

It is well known that a weakly almost periodic operator T in a Banach space is mean ergodic, and in the complex case, also λT is mean ergodic for every |λ|=1. We prove that a positive contraction on L 1 is weakly almost periodic if (and only if) it is mean ergodic. An example shows that without positivity the result is false. In order to construct a contraction T on a complex L 1 such that λT is mean ergodic whenever |λ|=1, but T is not weakly almost periodic, we prove the following: Let τ be an invertible...

Weighted Frobenius-Perron operators and their spectra

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2017)

Mathematica Bohemica

First, some classic properties of a weighted Frobenius-Perron operator 𝒫 ϕ u on L 1 ( Σ ) as a predual of weighted Koopman operator W = u U ϕ on L ( Σ ) will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of 𝒫 ϕ u under certain conditions.

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