Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Note on product formulas for operator semigroups - MaRDI portal

Note on product formulas for operator semigroups

From MaRDI portal
Publication:2527389

DOI10.1016/0022-1236(68)90020-7zbMath0157.21501OpenAlexW2061273628MaRDI QIDQ2527389

Paul R. Chernoff

Publication date: 1968

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(68)90020-7




Related Items

Error bounds for Trotter-type formulas for self-adjoint operatorsQuasi-Feynman formulas -- a method of obtaining the evolution operator for the Schrödinger equationDifferential equations in a Banach spaceA general Trotter--Kato formula for a class of evolution operatorsCentral limit theorems for random evolutionsViscous Hamilton-Jacobi equations in exponential Orlicz heartsRandom vortex methods for the Navier-Stokes equationTrace norm convergence of exponential product formulaSome recent progress on stochastic heat equationsCounterexamples to the Trotter formula in locally convex spacesMarkov approximations of the evolution of quantum systemsChernoff iterations as an averaging method for random affine transformationsDynamics of a quantum particle with discontinuous position-dependent massError estimate in operator norm for Trotter-Kato product formulaA generalization of Chernoff's product formula for time-dependent operatorsSome variations on Kac's formula for Brownian motionSemigroups of linear operators on \(p\)-Fréchet spaces, \(0<p<1\)Diffusion and quantum dynamics on graphsInfinite-dimensional evolution equations and the representation of their solutions in the form of Feynman integralsRate of convergence of Feynman approximations of semigroups generated by the oscillator HamiltonianPoissonmasse auf lokalkompakten HalbgruppenFeynman formula for Schrödinger-type equations with time- and space-dependent coefficientsVan Hove limit for infinite systemsFeynman description of the one-dimensional dynamics of particles whose masses piecewise continuously depend on coordinatesOn explicit representation and approximations of Dirichlet-to-Neumann semigroupApproximation of unbounded functions and applications to representations of semigroupsOperator splittings and spatial approximations for evolution equationsGeneralization of the Trotter-Lie formulaChernoff approximations for nonstationary random walk modelingSome developments in semigroups of operators since Hille-PhillipsSpeed of convergence of Chernoff approximations to solutions of evolution equationsMultiplicative partial integration and the Trotter product formulaStochastic processes on the group of orthogonal matrices and evolution equations describing themQuantum anomalies via differential properties of Lebesgue-Feynman generalized measuresUniform product formulae with application to the Feynman-Nelson integral for open systemsFeynman formulas generated by self-adjoint extensions of the Laplace operatorFeynman formulas for the diffusion of particles with position-dependent massQuasi-sectorial contractionsTrotter--Kato product formula and fractional powers of self-adjoint generators.On operator-norm approximation of some semigroups by quasi-sectorial operators.On transition semigroups of \((A,\mathbf\Psi)\)-superprocesses with immigrationAnalogue of Chernoff theorem for cylindrical pseudomeasuresExistence and stability of traveling pulse solutions of the FitzHugh-Nagumo equationFeynman formulas as a method of averaging random HamiltoniansInfinite-dimensional Schrödinger equations with polynomial potentials and Feynman path integralsA Trotter--Kato product formula for a class of non-autonomous evolution equationsTosio Kato's work on non-relativistic quantum mechanics. ISolution of the Schrödinger equation with the use of the translation operatorOperator approach to weak convergence of measures and limit theorems for random operatorsFeynman and quasi-Feynman formulas for evolution equationsRandom quantization of Hamiltonian systemsChernoff equivalence for shift operators, generating coherent states in quantum opticsAnalogues of Feynman formulas for ill-posed problems associated with the Schrödinger equationApproximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)Integrable QFT and Longo-Witten endomorphismsA probabilistic variant of Chernoff's product formulaRemarks on the Trotter-Kato product formula for unitary groupsDiffusion on Riemannian manifolds and integration with respect to anticommuting variablesMarkovian master equationsApproximation of the semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann spaceMarkovian master equations. IISemigroup-theoretic proofs of the central limit theorem and other theorems of analysisConvergence and approximation of semigroups of Lipschitz operatorsApproximately reducing subspaces for unbounded linear operatorsA Trotter-Lie formula for compactly generated semigroups of nonlinear operatorsOn the convergence of the method of weak approximation in a reflexive Banach spaceA product formula for semigroups of Lipschitz operators associated with semilinear evolution equations of parabolic typeProduct approximations for solutions to a class of evolution equations in Hilbert spaceNote on a product formula related to quantum Zeno dynamicsHigher order abstract Cauchy problemsIrreversible dynamics of infinite Fermion systemsTheorem about completeness of quantum mechanical motion groupEssential self-adjointness of semibounded operatorsProduct formulas in the framework of mean ergodic theoremsFeynman-Chernoff iterations and their applications in quantum dynamicsFeynman formulas generated by self-adjoint extensions of the LaplacianDirichlet-to-Neumann semigroup acts as a magnifying glassProduct approximations for a class of quantum anharmonic oscillatorsAnalyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescriptionQuantum Zeno effect in open quantum systemsTime-slicing approximation of Feynman path integrals on compact manifoldsA central limit theorem for products of dependent random linear and nonlinear operatorsA generalization of sectorial and quasi-sectorial operatorsMehler semigroups, Ornstein-Uhlenbeck processes and background driving Lévy processes on locally compact groups and on hypergroupsFeynman-Kac and Feynman formulas for evolution pseudodifferential equations in superspaceStability of the Peaceman-Rachford approximationAn approximation theorem for semigroups of growth order alpha and an extension of the Trotter-Lie formulaApproximation of operator semigroups using linear-fractional operator functions and weighted averagesNotes on the Chernoff product formulaFeynman formulas and path integrals for evolution equations with the Vladimirov operatorA remark on operator-norm convergence of Trotter-Kato product formulaA counterexample for the Trotter product formulaLimit distribution for compositions of random operatorsTrotter product formulae for \(\ast\)-automorphisms of quantum lattice systemsOn the Feynman pathsProduct formulas for solutions of initial value partial differential equations. IOn product formulas for exponential functionsNumerical analysis of semilinear stochastic evolution equations in Banach spacesBrownian motion in infinite dimensional manifoldsRate of convergence of Chernoff approximations of operator \(C_0\)-semigroupsFast converging Chernoff approximations to the solution of heat equation with variable coefficient of thermal conductivityLp -approximations for solutions of parabolic differential equations on manifoldsFeynman averaging of semigroups generated by Schrödinger operatorsFunction integrals corresponding to a solution of the Cauchy-Dirichlet problem for the heat equation in a domain of a Riemannian manifoldSemigroup product formulas and addition of unbounded operatorsAveraging of random orthogonal transformations of domain of functionsTHERMAL QUANTUM FIELDS WITHOUT CUT-OFFS IN 1+1 SPACE-TIME DIMENSIONSThe fourth order accuracy decomposition scheme for an evolution problemNew method for constructing Chernoff functionsThe essential spectrum of Schrödinger operators with asymptotically constant magnetic fields on the Poincaré upper-half planeA new proof of the Lie–Trotter–Kato formula in Hadamard spacesPath integrals on manifolds with boundaryOperator Semigroups for Convergence AnalysisOptimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensionsCharacterisations of dilations via approximants, expectations, and functional calculiA product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equationsOld and new challenges in Hadamard spacesUnnamed ItemNonlinear semigroups built on generating families and their Lipschitz setsMarkov Processes With Lipschitz SemigroupsChernoff approximations of Feller semigroups in Riemannian manifoldsUnitary representation of walks along random vector fields and the Kolmogorov-Fokker-Planck equation in a Hilbert spaceCompositions of random processes in a Hilbert space and its limit distributionA trotter product formula for random matricesSpherical Means and Geodesic Chains on a Riemannian ManifoldМоделирование эволюции выборочных распределений случайных величин с помощью уравнения ЛиувилляA convergent family of diffusion processes whose diffusion coefficients divergeDynamical control of quantum systems in the context of mean ergodic theoremsThe Method of Chernoff ApproximationNonassociative addition of unbounded operators and a problem of Brezis and PazyCentral Limit Theorem for Products of Random MatricesUnnamed ItemAn Integral Formula for Multidimensional Evolution EquationsQuantum Zeno effect generalizedComplex classical fields: an exampleChernoff approximation of subordinate semigroupsCovariant path integrals on hyperbolic surfacesOperator-norm approximation of semigroups by quasi-sectorial contractionsAccretive perturbations and error estimates for the Trotter product formulaQuantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. IIA formula for the solution of the Navier-Stokes equations based on a method of ChorinPath integrals on manifolds by finite dimensional approximationHigh degree precision decomposition method for the evolution problem with an operator under a split formRepresentation of solutions to a heat conduction equation with Vladimirov's operator by functional integralsChernoff's theorem on one-parametric semigroupsAsymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spacesFeynman formulas and functional integrals for diffusion with drift in a domain on a manifoldInversion of Chernoff's theoremApproximations of self-adjoint \(C_0\)-semigroups in the operator-norm topologyNumerical analysis view on the general Trotter–Kato product formulaeFormulas that represent Cauchy problem solution for momentum and position Schrödinger equationDiffusion on a Hilbert space equipped with a shift- and rotation-invariant measureFeynman formulas and the law of large numbers for random one-parameter semigroupsA Lie product formula for one parameter groups of isometries on Banach spacesApproximation of semi-groups of nonlinear operatorsSolution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficientsSemigroups on nonlinear contractions on convex setsAccretive sets and differental equations in Banach spacesChernoff bounds for discriminating between two markov processesConvergence and approximation of semigroups of nonlinear operators in Banach spacesA general approach to approximation theory of operator semigroupsHypercontra ctive semigroups and two dimensional self-coupled Bose fieldsAddition in a class of nonlinear Stieltjes integratorsThe Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. IEine Produktformel für Halbgruppen von Wahrscheinlichkeitsmaßen auf Lie-GruppenFinite dimensional semigroups of unitary endomorphisms of standard subspacesOn product formulas for nonlinear semigroupsApproximation of abstract Cauchy problems for dissipative operators with respect to metric-like functionalsTosio Kato’s work on non-relativistic quantum mechanics, Part 2Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equationsExplicit formula for evolution semigroup for diffusion in Hilbert spaceRepresentation of solutions of the Cauchy problem for a one-dimensional Schrödinger equation with a smooth bounded potential by quasi-Feynman formulaeMonotone increment processes, classical Markov processes, and Loewner chainsWiener and Poisson process regularization for coherent-state path integrals



Cites Work


This page was built for publication: Note on product formulas for operator semigroups