Resolvents of R-diagonal Operators

General Resolvents for Monotone Operators: Characterization and Extension

Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood and analyzed from the alternative viewpoint of firmly nonexpansive mappings, which were found to be precisely the resolvents of monotone operators. For examp...

Iterative Convergence of Resolvents of Maximal Monotone Operators Perturbed by the Duality Map in Banach Spaces

For a maximal monotone operator T in a Banach space an iterative solution of 0 ∈ Tx has been found through weak and strong convergence of resolvents of these operators. Identity mapping in the definition of resolvents has been replaced by the duality mapping. Solution after finite steps has also been established.

The Spectra of Operators Having Resolvents of First-order Growth^)

Laplacians on Metric Graphs: Eigenvalues, Resolvents and Semigroups

The main objective of the present work is to study the negative spectrum of (differential) Laplace operators on metric graphs as well as their resolvents and associated heat semigroups. We prove an upper bound on the number of negative eigenvalues and a lower bound on the spectrum of Laplace operators. Also we provide a sufficient condition for the associated heat semigroup to be positivity pre...

On Generalized Resolvents and Characteristic Matrices of Differential Operators

The main objects of our considerations are differential operators generated by a formally selfadjoint differential expression of an even order on the interval [0, b〉 (b ≤ ∞) with operator valued coefficients. We complement and develop the known Shtraus’ results on generalized resolvents and characteristic matrices of the minimal operator L0. Our approach is based on the concept of a decomposing...