L p Spectral Theory of Higher-Order Elliptic Differential Operators
From MaRDI portal
Publication:4399260
DOI10.1112/S002460939700324XzbMath0955.35019OpenAlexW2125327383MaRDI QIDQ4399260
Publication date: 21 February 2001
Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/s002460939700324x
eigenvaluessemigroupsground stateeigenfunctionsisoperimetric problemfunctional calculusheat kernelsRellich inequalityconical pointsspectral independenceHelffer-Sjöstrand calculus
General topics in linear spectral theory for PDEs (35P05) PDEs with low regular coefficients and/or low regular data (35R05) Schrödinger operator, Schrödinger equation (35J10) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Higher-order elliptic equations (35J30) Higher-order parabolic equations (35K25)
Related Items
Convergence of spectral expansions related to elliptic operators with singular coefficients, \(L^p\) spectral theory and heat dynamics of locally symmetric spaces, Spectral theory for perturbed Krein Laplacians in nonsmooth domains, The Holder continuity of the solutions to quasi-linear system of elliptic partial differential equations with singular coefficients, Eigenvalue asymptotics and exponential decay of eigenfunctions for the fourth order Schrödinger type operator, Smooth function extension based on high dimensional unstructured data, Rs-bounded H∞-calculus for sectorial operators via generalized Gaussian estimates, \(L^p\)-spectrum of the Dirac operator on products with hyperbolic spaces, The spectrum and heat dynamics of locally symmetric spaces of higher rank, Higher-order parabolic Schrödinger operators on Lebesgue spaces, Unnamed Item, \(L^{p}\) estimates for fractional Schrödinger operators with Kato class potentials, Unnamed Item, Malliavin calculus of Bismut type for an operator of order four on a Lie group, Time-step heat problem on the mesh: asymptotic behavior and decay rates, Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes, Regularity property of some operators on Lipschitz spaces and homogeneous Lipschitz spaces associated with biharmonic operator, Green's function estimates for elliptic differential operators with singular coefficients and absolute convergence of Fourier series, Local Hardy spaces associated with inhomogeneous higher order elliptic operators, Characterizations of Hardy spaces associated to higher order elliptic operators, Approximate Quadrature Measures on Data-Defined Spaces, A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel, Marcinkiewicz-Zygmund measures on manifolds, \(\varepsilon\)-coverings of Hölder-Zygmund type spaces on data-defined manifolds, Schrödinger operators in the twentieth century, Perturbation of the Malliavin Calculus of Bismut type for a large order on a Lie group, Optimal spectral approximation of \(2 n\)-order differential operators by mixed isogeometric analysis, Convoluted \(C\)-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines, Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation, Green's function and convergence of Fourier series for elliptic differential operators with potential from Kato space, The Schrödinger operator on the energy space: Boundedness and compactness criteria, On the index and spectrum of differential operators on ℝ^{ℕ}, The \(L^p\) resolvents of second-order elliptic operators of divergence form under the Dirichlet condition, A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains, Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems, An efficient direct solver for a class of mixed finite element problems, A generalized diffusion frame for parsimonious representation of functions on data defined manifolds, Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems, A domain description and Green's function estimates up to the boundary for elliptic operator with singular potential, Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients, Large time behaviour for the heat equation on \(\mathbb{Z} \), moments and decay rates, Minimum Sobolev norm interpolation of scattered derivative data, On semigroups generated by sums of even powers of Dunkl operators, Boundedness of differential transforms for the heat semigroup generated by biharmonic operator, Coincidence of weighted Hardy spaces associated with higher-order Schrödinger operators, Davies’ method for heat-kernel estimates: An extension to the semi-elliptic setting, Partial differential equations in the 20th century, Gaussian estimates with best constants for higher-order Schrödinger operators with Kato potentials, Convolution powers of complex functions on, Positive-Homogeneous Operators, Heat Kernel Estimates and the Legendre-Fenchel Transform, On the approximation of Finsler metrics on Euclidean domains, Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator, On the heat equation with a time-dependent singular potential, Local limit theorems for complex functions on \(\mathbb{Z}^d\), On the \(L^p\) spectrum of the Dirac operator, A Class of Non-Markovian Pseudo-differential Operators of Lévy Type, The \(L ^{p}\) resolvents of elliptic operators with uniformly continuous coefficients.
