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A C * -algebraic Schoenberg theorem

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Donald W. Robinson (1984)

Annales de l'institut Fourier

Let 𝔄 be a C * -algebra, G a compact abelian group, τ an action of G by * -automorphisms of 𝔄 , 𝔄 τ the fixed point algebra of τ and 𝔄 F the dense sub-algebra of G -finite elements in 𝔄 . Further let H be a linear operator from 𝔄 F into 𝔄 which commutes with τ and vanishes on 𝔄 τ . We prove that H is a complete dissipation if and only if H is closable and its closure generates a C 0 -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...

A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation

O. Awono, J. Tagoudjeu (2010)

Mathematical Modelling of Natural Phenomena

We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...

Accretive approximation in C*-algebras

Reiner Berntzen (1996)

Studia Mathematica

The problem of approximation by accretive elements in a unital C*-algebra suggested by P. R. Halmos is substantially solved. The key idea is the observation that accretive approximation can be regarded as a combination of positive and self-adjoint approximation. The approximation results are proved both in the C*-norm and in another, topologically equivalent norm.

Consistent models for electrical networks with distributed parameters

Corneliu A. Marinov, Gheorghe Moroşanu (1992)

Mathematica Bohemica

A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form L 2 ( 0 , T ; H 1 ) , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.

Domaine de la racine carrée de certains opérateurs différentiels accrétifs

Ronald R. Coifman, D. G. Deng, Yves Meyer (1983)

Annales de l'institut Fourier

Les racines carrées d’opérateurs différentiels accrétifs ont été définies et étudiées par Kato. Dans le cas d’opérateurs différentiels à coefficients C , les racines carrées sont des opérateurs pseudo-différentiels. Le cas des opérateurs différentiels à coefficients mesurables et bornés conduit à des racines carrées au-delà des opérateurs pseudo-différentiels. Ces nouveaux opérateurs s’étudient grâce à des mesures de Carleson.

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint h –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

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