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Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

Boundary Value Problems, 2020
In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed.
Maozhu Zhang, Kun Li, Hongxiang Song
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Uniqueness of DRS as the 2 operator resolvent-splitting and impossibility of 3 operator resolvent-splitting [PDF]

Mathematical Programming, 2019
Published in Mathematical Programming (updated version with corrected typo)
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Resolvent positive linear operators exhibit the reduction phenomenon [PDF]

Proceedings of the National Academy of Sciences, 2012
The spectral bound, s ( αA  +  βV ), of a combination of a resolvent positive linear operator A and an operator of multiplication V , was shown by Kato to be convex in .
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Dichotomy and H^infinity functional calculi

Electronic Journal of Differential Equations, 1995
densely defined closed operator on a Banach space is studied. We give conditions under which an operator with an $H^infty$ functional calculus has dichotomy.
R. DeLaubenfels, Y. Latushkin
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Hill's equation for a homogeneous tree

Electronic Journal of Differential Equations, 1997
The analysis of Hill's operator $-D^2 + q(x)$ for $q$ even and periodic is extended from the real line to homogeneous trees ${cal T}$. Generalizing the classical problem, a detailed analysis of Hill's equation and its related operator theory on $L^2({cal
Robert Carlson
doaj  

Study of Second-Order Differential Operators on Graphs with Small Edges

Mathematics
In this work, we investigate a Schrödinger operator defined on a model graph containing small loops, under the assumption that the standard nonresonance condition—typically ensuring the holomorphic dependence of the resolvent for elliptic operators on ...
Maral Konyrkulzhayeva, Gauhar Auzerkhan
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A partial factorization of the powersum formula

International Journal of Mathematics and Mathematical Sciences, 2004
For any univariate polynomial P whose coefficients lie in an ordinary differential field 𝔽 of characteristic zero, and for any constant indeterminate α, there exists a nonunique nonzero linear ordinary differential operator ℜ of finite order such that ...
John Michael Nahay
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Regularity of mild solutions to fractional Cauchy problems with Riemann-Liouville fractional derivative

Electronic Journal of Differential Equations, 2014
As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic alpha-order fractional resolvent which is defined in terms of Mittag-Leffler function and ...
Ya-Ning Li, Hong-Rui Sun
doaj  

The Classical Geometry of Chaotic Green Functions and Wigner Functions

Physics
Semiclassical (SC) approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in the phase space but such surface is not available for chaotic systems.
Alfredo M. Ozorio de Almeida
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Approximation solution for system of generalized ordered variational inclusions with ⊕ operator in ordered Banach space

Journal of Inequalities and Applications, 2017
The resolvent operator approach is applied to address a system of generalized ordered variational inclusions with ⊕ operator in real ordered Banach space. With the help of the resolvent operator technique, Li et al. (J. Inequal. Appl.
Mohd. Sarfaraz, MK Ahmad, A Kılıçman
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