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A study of resolvent set for a class of band operators with matrix elements

Andrey Osipov (2016)

Concrete Operators

For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.

A survey of certain trace inequalities

Dénes Petz (1994)

Banach Center Publications

This paper concerns inequalities like TrA ≤ TrB, where A and B are certain Hermitian complex matrices and Tr stands for the trace. In most cases A and B will be exponential or logarithmic expressions of some other matrices. Due to the interest of the author in quantum statistical mechanics, the possible applications of the trace inequalities will be commented from time to time. Several inequalities treated below have been established in the context of Hilbert space operators or operator algebras....

A unified analysis of elliptic problems with various boundary conditions and their approximation

Jérôme Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin (2020)

Czechoslovak Mathematical Journal

We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue-Sobolev spaces on a bounded domain. We apply this abstract setting to the numerical approximation of Leray-Lions type problems, which include in particular linear diffusion. The main interest of the abstract setting is to provide a unified convergence analysis that simultaneously covers (i) all usual boundary conditions, (ii)...

A useful algebra for functional calculus

Mohammed Hemdaoui (2019)

Mathematica Bohemica

We show that some unital complex commutative LF-algebra of 𝒞 ( ∞ ) ℕ -tempered functions on ℝ + (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

Evgenii Pustylnik (2001)

Czechoslovak Mathematical Journal

The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.

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