2015, Mathematical surveys and monographs, ISBN 1470425580, Volume 207, xii, 479

Book

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

( 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

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

In this work, the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems in a Banach space...

Fractional integro-differential systems | Nonlocal and impulsive conditions | Controllability | Fixed point theorem | [formula omitted]-resolvent family | (α u) -resolvent family | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | Non local and impulsive conditions | (alpha, u)-resolvent family | UNIQUENESS | Mathematical analysis | Evolution | Calculus | Mathematical models | Banach space | Delay

Fractional integro-differential systems | Nonlocal and impulsive conditions | Controllability | Fixed point theorem | [formula omitted]-resolvent family | (α u) -resolvent family | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | Non local and impulsive conditions | (alpha, u)-resolvent family | UNIQUENESS | Mathematical analysis | Evolution | Calculus | Mathematical models | Banach space | Delay

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

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

Eigenfunctions | Resolvent | Constant curvature

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 06/2016, Volume 289, Issue 8-9, pp. 1052 - 1099

We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define Neumann and Dirichlet boundary...

abstract Dirichlet problem | Boundary triples | Krein‐type resolvent formulas | variational Dirichlet‐to‐Neumann operator | Zaremba problem | 47B65 | spectral characterisation | 47A10 | 35J25 | 47F05 | abstract boundary value problems | Variational Dirichlet-to-Neumann operator | Spectral characterisation | Abstract boundary value problems | Abstract Dirichlet problem | Krein-type resolvent formulas | SPECTRAL THEORY | SECTORIAL OPERATORS | GENERALIZED RESOLVENTS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | MATHEMATICS | POINT INTERACTIONS | RESOLVENT FORMULAS | DIRICHLET | variational Dirichlet-to-Neumann operator | DIFFERENTIAL-OPERATORS | SCHRODINGER-OPERATORS

abstract Dirichlet problem | Boundary triples | Krein‐type resolvent formulas | variational Dirichlet‐to‐Neumann operator | Zaremba problem | 47B65 | spectral characterisation | 47A10 | 35J25 | 47F05 | abstract boundary value problems | Variational Dirichlet-to-Neumann operator | Spectral characterisation | Abstract boundary value problems | Abstract Dirichlet problem | Krein-type resolvent formulas | SPECTRAL THEORY | SECTORIAL OPERATORS | GENERALIZED RESOLVENTS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | MATHEMATICS | POINT INTERACTIONS | RESOLVENT FORMULAS | DIRICHLET | variational Dirichlet-to-Neumann operator | DIFFERENTIAL-OPERATORS | SCHRODINGER-OPERATORS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 06/2015, Volume 474, pp. 44 - 109

The main result of this paper is a new representation of Yu.M. Dyukarev's resolvent matrix for the non-degenerate truncated matricial version of the classical...

Dyukarev's resolvent matrix | Orthogonal matrix polynomials | Kovalishina's resolvent matrix | Non-degenerate truncated matricial Stieltjes moment problem | Matrix continued fractions | Non-degenerate truncated matricial Hamburger moment problem | Dyukarevs resolvent matrix | Kovalishinas resolvent matrix | MATHEMATICS, APPLIED | DEFINITE SEQUENCES | THEOREM | Stieltjes moment problem | NONDEGENERATE | INTERPOLATION | MATHEMATICS | ASYMPTOTICS | Hamburger moment problem | Non-degenerate truncated matricial

Dyukarev's resolvent matrix | Orthogonal matrix polynomials | Kovalishina's resolvent matrix | Non-degenerate truncated matricial Stieltjes moment problem | Matrix continued fractions | Non-degenerate truncated matricial Hamburger moment problem | Dyukarevs resolvent matrix | Kovalishinas resolvent matrix | MATHEMATICS, APPLIED | DEFINITE SEQUENCES | THEOREM | Stieltjes moment problem | NONDEGENERATE | INTERPOLATION | MATHEMATICS | ASYMPTOTICS | Hamburger moment problem | Non-degenerate truncated matricial

Journal Article

Asian Journal of Control, ISSN 1561-8625, 03/2019, Volume 21, Issue 2, pp. 725 - 748

In this paper, we investigate a new class of fractional impulsive stochastic partial integro‐differential equations with infinite delay in Hilbert spaces. By...

Fractional impulsive stochastic partial integro‐differential equations | optimal mild solutions | controllability | fixed point | analytic α‐resolvent operators | analytic α-resolvent operators | Fractional impulsive stochastic partial integro-differential equations | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | EVOLUTION-EQUATIONS | PSEUDO | UNIQUENESS | SYSTEMS | analytic alpha-resolvent operators | APPROXIMATE CONTROLLABILITY | RESOLVENT OPERATORS | AUTOMATION & CONTROL SYSTEMS | NONLOCAL CONDITIONS | Computer science | Differential equations | College teachers

Fractional impulsive stochastic partial integro‐differential equations | optimal mild solutions | controllability | fixed point | analytic α‐resolvent operators | analytic α-resolvent operators | Fractional impulsive stochastic partial integro-differential equations | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | EVOLUTION-EQUATIONS | PSEUDO | UNIQUENESS | SYSTEMS | analytic alpha-resolvent operators | APPROXIMATE CONTROLLABILITY | RESOLVENT OPERATORS | AUTOMATION & CONTROL SYSTEMS | NONLOCAL CONDITIONS | Computer science | Differential equations | College teachers

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2018, Volume 21, Issue 6, pp. 1542 - 1564

This paper is devoted to the inverse generator problem in the setting of generators of integrated resolvent operator functions. It is shown that if the...

integrated semigroups | inverse operator | times resolvent families | well-posedness | 47D62 | 34A08 | integrated cosine operator functions | 47D06 | 47D99 | abstract fractional Cauchy problem | generators | integrated resolvent operator function | 47D09 | α-times resolvent families | EXISTENCE | MATHEMATICS, APPLIED | CAUCHY-PROBLEM | alpha-times resolvent families | MATHEMATICS | SEMIGROUPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | Operators (mathematics) | Generators | Decay rate | Mathematical analysis | Bessel functions | Cauchy problem | Mathematics - Functional Analysis

integrated semigroups | inverse operator | times resolvent families | well-posedness | 47D62 | 34A08 | integrated cosine operator functions | 47D06 | 47D99 | abstract fractional Cauchy problem | generators | integrated resolvent operator function | 47D09 | α-times resolvent families | EXISTENCE | MATHEMATICS, APPLIED | CAUCHY-PROBLEM | alpha-times resolvent families | MATHEMATICS | SEMIGROUPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | Operators (mathematics) | Generators | Decay rate | Mathematical analysis | Bessel functions | Cauchy problem | Mathematics - Functional Analysis

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

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

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

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

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

Convergence theorem | Resolvent | Equilibrium problem | Banach space | Relatively nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

16.
Full Text
Irreducible recurrence, ergodicity, and extremality of invariant measures for resolvents

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

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

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

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

Existence result | Fractional stochastic differential equation | Resolvent operators | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | EVOLUTION INCLUSIONS | MILD SOLUTIONS | Differential equations

Journal Article

20.
Full Text
On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 11/2019, Volume 398, pp. 208 - 218

We consider the scattering problem for the nonlinear Schrödinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved...

Resolvent estimates | Scattering problem | Strichartz estimates | Nonlinear Schrödinger equation | Time decay estimates | EXISTENCE | LIFE-SPAN | STRICHARTZ | MATHEMATICS, APPLIED | LARGE TIME | NONEXISTENCE | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | Nonlinear Schrodinger equation | WAVE-OPERATORS | PHYSICS, MATHEMATICAL | HEAT KERNELS | RESOLVENT | BOUNDS | DISSIPATIVE NONLINEARITY

Resolvent estimates | Scattering problem | Strichartz estimates | Nonlinear Schrödinger equation | Time decay estimates | EXISTENCE | LIFE-SPAN | STRICHARTZ | MATHEMATICS, APPLIED | LARGE TIME | NONEXISTENCE | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | Nonlinear Schrodinger equation | WAVE-OPERATORS | PHYSICS, MATHEMATICAL | HEAT KERNELS | RESOLVENT | BOUNDS | DISSIPATIVE NONLINEARITY

Journal Article

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