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Semigroup Forum, ISSN 0037-1912, 2/2010, Volume 80, Issue 1, pp. 121 - 142
In this paper we introduce three kinds of resolvent families defined by purely algebraic equations, which extend the classical semigroup property and Cosine... 
( α , β )-resolvent operator functions | Mathematics | Generators | Algebra | Analyticity criteria | α -times resolvent families | (α,β)-resolvent operator functions | α-times resolvent families | alpha-times resolvent families | MATHEMATICS | APPROXIMATION | FAMILIES | (alpha, beta)-resolvent operator functions | VOLTERRA-EQUATIONS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 372, Issue 7, pp. 5243 - 5262
In this note, uniform bounds of the Birman-Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound... 
MATHEMATICS | ROUGH | Discrete Schrodinger operators | RESOLVENT | EQUATIONS | resolvents | limiting absorption principle | SOBOLEV INEQUALITIES | SCHRODINGER-OPERATORS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 1442 - 1450
Journal Article
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 05/2019, Volume 2019, Issue 10, pp. 3242 - 3264
Let f : X -> CP1 be a meromorphic function of degree N with simple poles and simple critical points on a compact Riemann surface X of genus g and let m be the... 
MATHEMATICS | RESOLVENT | TAU-FUNCTIONS | SURFACES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 12/2014, Volume 267, Issue 12, pp. 4635 - 4666
We prove families of uniform (Lr,Ls) resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier... 
Eigenfunctions | Resolvent | Constant curvature
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 69, Issue 11, pp. 3692 - 3705
We introduce the concept of α -resolvent families to prove the existence of almost automorphic mild solutions to the differential equation D t α u ( t ) = A u... 
Almost automorphic function | Resolvent family | Semilinear differential equations | Fractional derivative | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | Almost automorphic functions | RESOLVENT FAMILIES | ASYMPTOTIC-BEHAVIOR
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2019, Volume 473, Issue 1, pp. 215 - 257
We study scattering for the couple (AF,A0) of Schrödinger operators in L2(R3) formally defined as A0=−Δ+αδπ0 and AF=−Δ+αδπF, α>0, where δπF is the Dirac... 
Point interactions supported by unbounded hypersurfaces | Kreĭn's resolvent formulae | Scattering theory | MATHEMATICS | MATHEMATICS, APPLIED | Krein's resolvent formulae | BOUND-STATES | LIMITING ABSORPTION PRINCIPLE | OPERATORS
Journal Article
Communications in mathematical physics, ISSN 0010-3616, 06/2020, Volume 376, Issue 3, pp. 2301 - 2308
We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical... 
OPERATOR | RESOLVENT | BOUNDS | POLES | WAVE-EQUATION | PHYSICS, MATHEMATICAL | RESONANCES
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2012, Volume 19, Issue 2, pp. 309 - 324
A well-known result of Jaffard states that an arbitrary region on a torus controls, in the L-2 sense, solutions of the free stationary and dynamical... 
MATHEMATICS | RESOLVENT | EIGENFUNCTIONS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 1, pp. 45 - 57
In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of... 
Convergence theorem | Resolvent | Equilibrium problem | Banach space | Relatively nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2018, Volume 128, Issue 4, pp. 1405 - 1437
We analyze the transience, recurrence, and irreducibility properties of general sub-Markovian resolvents of kernels and their duals, with respect to a fixed... 
Markov process | Irreducibility | Recurrence | Resolvent | Invariant measure | Dirichlet form | POLAR SETS | THEOREM | SPACES | EQUATIONS | STATISTICS & PROBABILITY | LOGARITHMIC SOBOLEV INEQUALITY | L-P-RESOLVENTS | CONSERVATIVENESS
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 23, pp. 7103 - 7136
We investigate the high-energy limits of the moments of Eisenstein series, when these functions are considered as real random variables over a compact subset... 
MATHEMATICS | EIGENFUNCTIONS | COMPLETE SPACES | RESOLVENT
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2018, Volume 370, Issue 11, pp. 7761 - 7787
For a fixed right process X we investigate those functions u for which u(X) is a quasimartingale. We prove that u(X) is a quasimartingale if and only if u is... 
Markov process | Quasimartingale | Fukushima decomposition | Excessive function | Smooth measure | Dirichlet form | Semimartingale | MATHEMATICS | SUBORDINATION | RESOLVENTS | excessive function | SENSE | quasimartingale | smooth measure
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2013, Volume 81, pp. 70 - 86
The fractional stochastic differential equations have wide applications in various fields of science and engineering. This paper addresses the issue of... 
Existence result | Fractional stochastic differential equation | Resolvent operators | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | EVOLUTION INCLUSIONS | MILD SOLUTIONS | Differential equations
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 11/2019, Volume 398, pp. 208 - 218
Journal Article
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