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Generalized Resolvents of Symmetric Operators
Mathematical Notes, 2003The Krein formula for generalized resolvents is one of the highlights of the theory of extensions of symmetric operators in Hilbert spaces. In the present paper, the authors give another more general version of such a formula for generalized \(U\)-resolvents of the isometric operator \(V\). Each boundary triple \(\Pi\) of \(\{V,V^{-1}\}\) generates the
Malamud, M. M., Mogilevskii, V. I.
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On the Formulation of the Resolvent Operator for Compressible Flows
AIAA SCITECH 2024 ForumThis paper investigates the non-uniqueness of resolvent analysis in the context of compressible fluid flows. Specifically, we compare two mathematically equivalent formulations of the compressible Navier-Stokes equations (NSEs) in two sets of flow ...
Diganta Bhattacharjee, Maziar S. Hemati
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Proceedings of the London Mathematical Society, 1987
Let A be a resolvent positive (linear) operator (i.e., \((\lambda -A)^{- 1}\) exists and is positive for \(\lambda >\lambda_ 0)\) on a Banach lattice E. Even though no norm condition on the resolvent is demanded, a theory is developed which - to a large extent - is analogous to the theory of positive \(C_ 0\)-semigroups.
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Let A be a resolvent positive (linear) operator (i.e., \((\lambda -A)^{- 1}\) exists and is positive for \(\lambda >\lambda_ 0)\) on a Banach lattice E. Even though no norm condition on the resolvent is demanded, a theory is developed which - to a large extent - is analogous to the theory of positive \(C_ 0\)-semigroups.
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About a complex operator resolvent
Russian Universities Reports. Mathematics, 2022A normed algebra of bounded linear complex operators acting in a complex normed space consisting of elements of the Cartesian square of a real Banach space is constructed. In this algebra, it is singled out a set of operators for each of which the real and imaginary parts commute with each other.
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H-Monotone operator and resolvent operator technique for variational inclusions
Applied Mathematics and Computation, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yaping Fang, N. Huang
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2017
This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ-L) R(μ) f = f, R(μ) is a right inverse for (μ-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions.
Charles L. Epstein, Rafe Mazzeo
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This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ-L) R(μ) f = f, R(μ) is a right inverse for (μ-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions.
Charles L. Epstein, Rafe Mazzeo
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Resolvents of Monotone Operators
2011Two quite useful single-valued, Lipschitz continuous operators can be associated with a monotone operator, namely its resolvent and its Yosida approximation. This chapter is devoted to the investigation of these operators. It exemplifies the tight interplay between firmly nonexpansive mappings and monotone operators.
Heinz H. Bauschke, Patrick L. Combettes
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Resolvent splitting for sums of monotone operators with minimal lifting
Mathematical programming, 2021In this work, we study fixed point algorithms for finding a zero in the sum of n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
Yura Malitsky, Matthew K. Tam
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Approximation processes for resolvent operators
Calcolo, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CAMPITI, Michele, TACELLI, CRISTIAN
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Strong Resolvent Convergence of Diffusion Operators
SIAM Journal on Mathematical Analysis, 1985Summary: It is shown that differential operators arising from boundary value problems with eigenvalue parameter in the boundary condition occur as the limits, in the sense of a generalized notion of strong resolvent convergence, of families of Sturm-Liouville operators modeling heat flow in a rod, where the diffusion coefficient becomes arbitrarily ...
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