Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 459, Issue 1, pp. 528 - 555

...∞ resolvent estimate for the bidomain operator by using a contradiction argument based on a blow-up argument...

Bidomain model | Resolvent estimates | Blow-up argument | ANALYTICITY | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | SPACES | REACTION-DIFFUSION SYSTEMS | MODEL | ELLIPTIC-OPERATORS | FRONT PROPAGATION | Wave propagation

Bidomain model | Resolvent estimates | Blow-up argument | ANALYTICITY | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | SPACES | REACTION-DIFFUSION SYSTEMS | MODEL | ELLIPTIC-OPERATORS | FRONT PROPAGATION | Wave propagation

Journal Article

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Full Text
Strichartz Estimate and Nonlinear Klein–Gordon Equation on Nontrapping Scattering Space

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2957 - 2984

.... We establish the global-in-time Strichartz estimate for Klein–Gordon equation without loss of derivative by using the microlocalized spectral measure of Laplacian...

Scattering manifold | 35S30 | Mathematics | 35Q40 | Scattering theory | Abstract Harmonic Analysis | Strichartz estimate | Fourier Analysis | Spectral measure | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Global existence | Differential Geometry | Dynamical Systems and Ergodic Theory | 47J35 | EXISTENCE | PARAMETRIX | SITTER | MATHEMATICS | REGULARITY | RESOLVENT | WAVE-EQUATIONS | OPERATORS | PROPAGATOR

Scattering manifold | 35S30 | Mathematics | 35Q40 | Scattering theory | Abstract Harmonic Analysis | Strichartz estimate | Fourier Analysis | Spectral measure | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Global existence | Differential Geometry | Dynamical Systems and Ergodic Theory | 47J35 | EXISTENCE | PARAMETRIX | SITTER | MATHEMATICS | REGULARITY | RESOLVENT | WAVE-EQUATIONS | OPERATORS | PROPAGATOR

Journal Article

Bulletin of mathematical sciences, ISSN 1664-3615, 2019, Volume 9, Issue 1, pp. 1950003 - 1950003-15

We extend the resolvent estimate on the sphere to exponents off the line [Formula: see text]. Since the condition...

Sphere | Resolvent estimate | Bourgain’s interpolation technique | MATHEMATICS | sphere | Bourgain's interpolation technique | resolvent estimate | bourgain’s interpolation technique

Sphere | Resolvent estimate | Bourgain’s interpolation technique | MATHEMATICS | sphere | Bourgain's interpolation technique | resolvent estimate | bourgain’s interpolation technique

Journal Article

Communications in mathematical physics, ISSN 1432-0916, 2019, Volume 376, Issue 3, pp. 2301 - 2308

We prove explicit semiclassical resolvent estimates for an integrable potential on the real line...

OPERATOR | RESOLVENT | BOUNDS | POLES | WAVE-EQUATION | PHYSICS, MATHEMATICAL | RESONANCES

OPERATOR | RESOLVENT | BOUNDS | POLES | WAVE-EQUATION | PHYSICS, MATHEMATICAL | RESONANCES

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 2018, Volume 110, Issue 3-4, pp. 137 - 161

.... In the current contribution we improve this result deriving estimates for the rate of convergence in terms of operator norms...

Crushed ice problem | Homogenization | Norm resolvent convergence | Varying Hilbert spaces | Operator estimates | LAPLACIAN | MATHEMATICS, APPLIED | homogenization | operator estimates | ERROR ESTIMATE | norm resolvent convergence | NORM-RESOLVENT CONVERGENCE | varying Hilbert spaces | SPECTRUM | DIRICHLET | ELLIPTIC-OPERATORS | Eigenvalues | Norms | Dirichlet problem | Hilbert space | Convergence

Crushed ice problem | Homogenization | Norm resolvent convergence | Varying Hilbert spaces | Operator estimates | LAPLACIAN | MATHEMATICS, APPLIED | homogenization | operator estimates | ERROR ESTIMATE | norm resolvent convergence | NORM-RESOLVENT CONVERGENCE | varying Hilbert spaces | SPECTRUM | DIRICHLET | ELLIPTIC-OPERATORS | Eigenvalues | Norms | Dirichlet problem | Hilbert space | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2016, Volume 439, Issue 1, pp. 103 - 124

We show H∞-functional calculus estimates for Tadmor–Ritt operators (also known as Ritt operators...

Ritt operator | Kreiss Matrix Theorem | Power-bounded operator | Functional calculus | Square function estimates | Tadmor–Ritt operator | Tadmor-Ritt operator | Analysis | Applied Mathematics | MATHEMATICS, APPLIED | RESOLVENT CONDITIONS | STABILITY | POWER-BOUNDED OPERATORS | TIME | ANALYTIC SEMIGROUPS | CONJECTURE | MATHEMATICS | MAXIMAL REGULARITY | DISCRETE | L-P-SPACES

Ritt operator | Kreiss Matrix Theorem | Power-bounded operator | Functional calculus | Square function estimates | Tadmor–Ritt operator | Tadmor-Ritt operator | Analysis | Applied Mathematics | MATHEMATICS, APPLIED | RESOLVENT CONDITIONS | STABILITY | POWER-BOUNDED OPERATORS | TIME | ANALYTIC SEMIGROUPS | CONJECTURE | MATHEMATICS | MAXIMAL REGULARITY | DISCRETE | L-P-SPACES

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 12/2017, Volume 42, Issue 12, pp. 1962 - 1981

We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifolds X ∘ . Let where Δ...

scattering manifold | Strichartz estimate | resolvent estimate | Mild trapped set | MATHEMATICS, APPLIED | DECAY | POTENTIALS | 35Q40 | MATHEMATICS | ASYMPTOTICALLY CONIC MANIFOLDS | WAVE-EQUATION | 42B37 | SEMICLASSICAL RESOLVENT | TRAPPED SETS | 47J35 | Operators (mathematics) | Scattering | Schroedinger equation

scattering manifold | Strichartz estimate | resolvent estimate | Mild trapped set | MATHEMATICS, APPLIED | DECAY | POTENTIALS | 35Q40 | MATHEMATICS | ASYMPTOTICALLY CONIC MANIFOLDS | WAVE-EQUATION | 42B37 | SEMICLASSICAL RESOLVENT | TRAPPED SETS | 47J35 | Operators (mathematics) | Scattering | Schroedinger equation

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7293 - 7333

...-square type potentials and includes several anisotropic potentials. We first prove weighted resolvent estimates, which are uniform with respect to the energy, with a large class of weight functions in Morrey-Campanato spaces...

Resolvent estimates | Strichartz estimates | Critical singularities | Schrödinger operator | MAGNETIC POTENTIALS | INEQUALITIES | PERTURBATIONS | critical singularities | CRITICAL DECAY | resolvent estimates | L-P | MATHEMATICS | DIMENSIONS | WEAKLY CONJUGATE OPERATOR | ENERGY ASYMPTOTICS | TIME-DECAY | Schrodinger operator | WAVE-EQUATION

Resolvent estimates | Strichartz estimates | Critical singularities | Schrödinger operator | MAGNETIC POTENTIALS | INEQUALITIES | PERTURBATIONS | critical singularities | CRITICAL DECAY | resolvent estimates | L-P | MATHEMATICS | DIMENSIONS | WEAKLY CONJUGATE OPERATOR | ENERGY ASYMPTOTICS | TIME-DECAY | Schrodinger operator | WAVE-EQUATION

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2018, Volume 264, Issue 6, pp. 3811 - 3835

We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent...

Resolvent estimates | Fractional elasticity | Gelfand transform | Homogenisation | Operator-norm convergence | INCLUSIONS | EQUATIONS | WELL-POSEDNESS | MATERIAL LAWS | MATHEMATICS | COEFFICIENTS | CONVERGENCE | ELLIPTIC-SYSTEMS

Resolvent estimates | Fractional elasticity | Gelfand transform | Homogenisation | Operator-norm convergence | INCLUSIONS | EQUATIONS | WELL-POSEDNESS | MATERIAL LAWS | MATHEMATICS | COEFFICIENTS | CONVERGENCE | ELLIPTIC-SYSTEMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 1, pp. 336 - 360

... resolvent estimates for the perturbed operator under the same assumptions about V.

Helmholtz equation | Resolvent estimates | Spectral Theory | Lamé operator | Lame operator | SCHRODINGER-EQUATIONS | MATHEMATICS | WAVE | MATHEMATICS, APPLIED

Helmholtz equation | Resolvent estimates | Spectral Theory | Lamé operator | Lame operator | SCHRODINGER-EQUATIONS | MATHEMATICS | WAVE | MATHEMATICS, APPLIED

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 2016, Volume 368, Issue 12, pp. 8755 - 8784

.... The key point of our work is to make a direct link between the problem and the weighted L-2 resolvent estimates parallel to(-Delta-z)(-1)f parallel to(L2...

Resolvent estimates | Unique continuation | Schrödinger equations | MATHEMATICS | STRICHARTZ | Schrodinger equations | INEQUALITIES | DECAY | unique continuation

Resolvent estimates | Unique continuation | Schrödinger equations | MATHEMATICS | STRICHARTZ | Schrodinger equations | INEQUALITIES | DECAY | unique continuation

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2018, Volume 275, Issue 8, pp. 1943 - 2014

In this paper, we prove global in time Strichartz estimates for the fractional Schrödinger operators, namely e−itΛgσ with σ∈(0,∞)\{1} and Λg:=−Δg where Δg is the Laplace...

Global in time Strichartz estimate | Fractional Schrödinger equation | Littlewood–Paley decomposition | Isozaki–Kitada parametrix | LOCAL ENERGY DECAY | Fractional Schrodinger equation | Isozaki-Kitada parametrix | CONIC MANIFOLDS | INTEGRALS | MATHEMATICS | Littlewood-Paley decornposition | SCATTERING MANIFOLDS | VARIABLE-COEFFICIENTS | RESOLVENT | NONTRAPPING METRICS | LONG-RANGE PERTURBATIONS | WAVE-EQUATION | OPERATORS | Analysis of PDEs | Mathematics

Global in time Strichartz estimate | Fractional Schrödinger equation | Littlewood–Paley decomposition | Isozaki–Kitada parametrix | LOCAL ENERGY DECAY | Fractional Schrodinger equation | Isozaki-Kitada parametrix | CONIC MANIFOLDS | INTEGRALS | MATHEMATICS | Littlewood-Paley decornposition | SCATTERING MANIFOLDS | VARIABLE-COEFFICIENTS | RESOLVENT | NONTRAPPING METRICS | LONG-RANGE PERTURBATIONS | WAVE-EQUATION | OPERATORS | Analysis of PDEs | Mathematics

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 05/2017, Volume 272, Issue 9, pp. 3904 - 3918

We prove Lp→Lp′ bounds for the resolvent of the Laplace–Beltrami operator on a compact Riemannian manifold of dimension n in the endpoint case p=2(n+1)/(n+3)....

Oscillatory integrals | Hadamard parametrix | Resolvent | Laplace–Beltrami operator | MATHEMATICS | CLUSTERS | OPERATORS | Laplace-Beltrami operator

Oscillatory integrals | Hadamard parametrix | Resolvent | Laplace–Beltrami operator | MATHEMATICS | CLUSTERS | OPERATORS | Laplace-Beltrami operator

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 12/2015, Volume 15, Issue 4, pp. 753 - 799

... Equations Exponentially weighted resolvent estimates for complex Ornstein–Uhlenbeck systems Denny Otten Abstract. In this paper, we study differential operators...

Analysis | Resolvent estimates | Exponentially weighted function spaces | Mathematics | Ornstein–Uhlenbeck semigroup | Heat kernel matrix | 35K45 (35J47, 35K08, 35B65, 35B45, 35B40) | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | RESPECT | DOMAIN | COEFFICIENTS | PHYSICS | L-P SPACES | ELLIPTIC-OPERATORS | FUNDAMENTAL-SOLUTIONS | Cytokinins | Mathematics - Analysis of PDEs

Analysis | Resolvent estimates | Exponentially weighted function spaces | Mathematics | Ornstein–Uhlenbeck semigroup | Heat kernel matrix | 35K45 (35J47, 35K08, 35B65, 35B45, 35B40) | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | RESPECT | DOMAIN | COEFFICIENTS | PHYSICS | L-P SPACES | ELLIPTIC-OPERATORS | FUNDAMENTAL-SOLUTIONS | Cytokinins | Mathematics - Analysis of PDEs

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 09/2018, Volume 43, Issue 9, pp. 1306 - 1362

.... We then classify the microlocal resolvent behavior associated to every possible type of critical value of the potential, and translate this into the associated resolvent estimates...

local smoothing | Damped wave equation | one dimensional Schrödinger operators | partially rectangular billiards | resolvent estimates | warped product | MATHEMATICS | MATHEMATICS, APPLIED | one dimensional Schrodinger operators | QUASIMODES | MANIFOLDS | EQUATION | Operators (mathematics) | Trapping | Decay rate | Asymptotic properties | Mathematical analysis | Spreading | Wave equations | Polynomials | Manifolds (mathematics)

local smoothing | Damped wave equation | one dimensional Schrödinger operators | partially rectangular billiards | resolvent estimates | warped product | MATHEMATICS | MATHEMATICS, APPLIED | one dimensional Schrodinger operators | QUASIMODES | MANIFOLDS | EQUATION | Operators (mathematics) | Trapping | Decay rate | Asymptotic properties | Mathematical analysis | Spreading | Wave equations | Polynomials | Manifolds (mathematics)

Journal Article

Potential Analysis, ISSN 0926-2601, 1/2019, Volume 50, Issue 1, pp. 107 - 133

.... We first establish L p -resolvent estimates on bounded domains having small Lipschitz constant when r / ( r − 1 ) < p < ∞ $r/(r-1) < p < \infty...

Geometry | Potential Theory | Functional Analysis | Dirichlet problems | Elliptic equations | Resolvent estimates | Probability Theory and Stochastic Processes | Mathematics | Lower order terms | 35J15 | 47A10 | 35J25 | MATHEMATICS | BMO COEFFICIENTS | SYSTEMS | OPERATORS

Geometry | Potential Theory | Functional Analysis | Dirichlet problems | Elliptic equations | Resolvent estimates | Probability Theory and Stochastic Processes | Mathematics | Lower order terms | 35J15 | 47A10 | 35J25 | MATHEMATICS | BMO COEFFICIENTS | SYSTEMS | OPERATORS

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2019, Volume 9, Issue 1, pp. 171 - 194

In this paper we prove a subelliptic resolvent estimate for a broad class of semiclassical non-self-adjoint Schrodinger operators with complex potentials when the spectral parameter is in a...

Resolvent estimate | Nonselfadjoint Schrödinger operator | Spectral theory | Schrödinger operator | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger operator | spectral theory | resolvent estimate | nonselfadjoint Schrodinger operator

Resolvent estimate | Nonselfadjoint Schrödinger operator | Spectral theory | Schrödinger operator | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger operator | spectral theory | resolvent estimate | nonselfadjoint Schrodinger operator

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 08/2015, Volume 269, Issue 3, pp. 633 - 682

We investigate L1(Rn)→L∞(Rn) dispersive estimates for the Schrödinger operator H=−Δ+V when there is an eigenvalue at zero energy and n...

Threshold eigenvalue | Dispersive estimates | Resolvent | OBSTRUCTIONS | EXPANSIONS | EQUATIONS | 4-DIMENSIONAL SCHRODINGER | SPECTRAL PROPERTIES | ZERO-ENERGY | MATHEMATICS | WAVE-FUNCTIONS | RESONANCE | TIME-DECAY | SCATTERING

Threshold eigenvalue | Dispersive estimates | Resolvent | OBSTRUCTIONS | EXPANSIONS | EQUATIONS | 4-DIMENSIONAL SCHRODINGER | SPECTRAL PROPERTIES | ZERO-ENERGY | MATHEMATICS | WAVE-FUNCTIONS | RESONANCE | TIME-DECAY | SCATTERING

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, pp. 438 - 474

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 2018, Volume 113, pp. 155 - 194

We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li–Yau estimate...

Heat kernel | Parabolic manifold | Manifold with ends | Integrated resolvent | BROWNIAN-MOTION | MATHEMATICS, APPLIED | INEQUALITY | NASH | MATHEMATICS | LOWER BOUNDS | OLD IDEAS | EQUATION | RIEMANNIAN-MANIFOLDS

Heat kernel | Parabolic manifold | Manifold with ends | Integrated resolvent | BROWNIAN-MOTION | MATHEMATICS, APPLIED | INEQUALITY | NASH | MATHEMATICS | LOWER BOUNDS | OLD IDEAS | EQUATION | RIEMANNIAN-MANIFOLDS

Journal Article

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