We prove Hölder-continuous dependence results for the difference between solutions of certain ill-posed and approximate well-posed problems in both Hilbert and Banach spaces. We use operator-theoretic methods, including C-semigroups, to treat the abstract Cauchy problem du dt = Au, u(0) = χ, 0 ≤ t < T, where the operator −A is the infinitesimal generator of a holomorphic semigroup.

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...

Let S be the multiplication operator by an independent variable x in L2(0, 1) and V be an integral operator of Volterra type. We find conditions for T := S + V to be similar to S and discuss some generalisations of the results obtained to an abstract setting.

This paper makes a proposal for introducing into the B Method [3] a new refinement operator dedicated to take into account distribution fro m the very specification level through all stepwise refinement process of B abstract machines towards actual implementations. Our operator expresses how a whole system composed of many concurrent and communicating processes can be designed by refinement. Su...

An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a single, common integration procedure over the original Lagrange multiplier variables that is completely independent of the general nature of the constraints. I...

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Abstract— The direct part of Stein’s lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein’s lemma without using Hiai-Petz’s theorem, along with an operator monotone function, and in addition it is also used to show a new proof of Hiai-Pet...

We examine linear, bounded, fixed operators as channels between continuous input functions and continuous output functions. The time-frequency waveform channel and continuous space channel are both related to an abstract operator viewpoint of communication channels. The properties of the operator required in order to allow valid capacity estimation are examined, and the modelling of noise in a ...

We introduce generalized operator valued Jost solutions of first order ill-posed differential equations on Hilbert spaces. We then construct an infinite dimensional Evans function for abstract differential equations as a 2– modified Fredholm determinant of the operator obtained by adding the values at zero of the generalized operator valued Jost solutions. Next, we prove a formula that connects...

SFB393/05-01 January 2005 Abstract The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in R. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the ...