Fractional powers of closed operators and the semigroups generated by them

DOI10.2140/pjm.1960.10.419zbMath0103.33502OpenAlexW2093169427MaRDI QIDQ774886

A. V. Balakrishnan

Publication date: 1960

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1960.10.419

zbMATH Keywords

functional analysis

Related Items

Nonlocal Cauchy problems for semilinear evolution equations, Study of an elliptic differential equation: Set in three habitats with skewness boundary conditions at the interfaces in \(L^q\) cases, Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation, An incomplete Cauchy problem, Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups, Factorized schemes for first and second order evolution equations with fractional powers of operators, A heat-viscoelastic structure interaction model with Neumann and Dirichlet boundary control at the interface: optimal regularity, control theoretic implications, Analytic semigroups generated by the dispersal process in two habitats incorporating individual behavior at the interface, Nonlocal general boundary value problems of elliptic type in \(L^p\) cases, Blowup for fractional NLS, Positivity and contractivity in the dynamics of clusters' splitting with derivative of fractional order, Exponentially convergent trapezoidal rules to approximate fractional powers of operators, On elliptic equations with general non-local boundary conditions in UMD spaces, The fractional Laplacian in power-weighted \(L^{p}\) spaces: integration-by-parts formulas and self-adjointness, On relating two approaches for fractional calculus, Short-range scattering of Hartree type fractional NLS, Weyl and Marchaud derivatives: a forgotten history, Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups, Fractional integration and differentiation of variable order: an overview, Scattering below ground state of focusing fractional nonlinear Schrödinger equation with radial data, On the relationship between the solutions of an abstract Euler-Poisson-Darboux equation and fractional powers of the operator coefficient in the equation, Continuous dependence results for inhomogeneous ill-posed problems in Banach space, Necessary and sufficient conditions for the solvability and maximal regularity of abstract differential equations of mixed type in Hölder spaces, New results on elliptic equations with nonlocal boundary coefficient-operator conditions in UMD spaces: noncommutative cases, Gaussian estimates of order \(\alpha\) and \(L^p\)-spectral independence of generators of \(C_{0}\)-semigroups, Fractional dynamics, irreversibility and ergodicity breaking, Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators, Optimal Landau-Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces, Characterizations of domains of fractional powers for non-negative operators, A mathematical analysis of fractional fragmentation dynamics with growth, Unified theory for abstract parabolic boundary problems - a semigroup approach, Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups., Ill-posed problems associated with sectorial operators in Banach space, Resolution, in \(L^{p}\)-spaces, of transmission problems set in an unbounded domains, Fractional Heisenberg equation, Fractional powers approach of operators for the solvability of some elliptic PDEs with variable operators coefficients, On the harmonic extension approach to fractional powers in Banach spaces, Some aspects of E. Hille's contribution to semi-group theory, From Sturm-Liouville problems to fractional and anomalous diffusions, Sur l'interpolation des opérateurs maximaux monotones, Finite element methods for fractional-order diffusion problems with optimal convergence order, Damping operators in continuum models of flexible structures: Explicit models for proportional damping in beam bending with end-bodies, A fractional power approach to fractional calculus, Existence results for a Michaud fractional, nonlocal, and randomly position structured fragmentation model, A resolvent approach to the real quantum plane, What is the fractional Laplacian? A comparative review with new results, Entire solutions of the abstract Cauchy problem, \(H^{\infty}\)-calculus for semigroup generators on BMO, On the Kato square root problem, Convergence rates for solutions of inhomogeneous ill-posed problems in Banach space with sufficiently smooth data, On some consequences of the solvability of the Caffarelli-Silvestre extension problem, On a cascade system of Schrödinger equations. Fractional powers approach, Fractional glassy relaxation and convolution modules of distributions, Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas, Smooth zero-contact-angle solutions to a thin-film equation around the steady state, Numerical solutions for fractional reaction-diffusion equations, Fractional generalized logistic equations with indefinite weight: quantitative and geometric properties, Functional inequalities for a class of nonlocal hypoelliptic equations of Hörmander type, Distributional fractional powers and Riesz fractional integrals, Spectral mapping theorem for fractional powers of linear relations, Space-time fractional equations and the related stable processes at random time, Kernel estimates and \(L^p\)-spectral independence of generators of \(C_0\)-semigroups, An application of the \(S\)-functional calculus to fractional diffusion processes, Probabilistic representation formula for the solution of fractional high-order heat-type equations, Incomplete iterated Cauchy problems, Puissances fractionnaires d'un opérateur générateur d'un semi-groupe distribution régulier, On fractional powers of generators of fractional resolvent families, Domaines d'opérateurs représentes comme intégrales de resolvantes, Numerical continuation for fractional PDEs: sharp teeth and bloated snakes, Fuzzy conformable fractional semigroups of operators, Analytic generators for one-parameter groups, Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator, Solvability of elliptic differential equations, set in three habitats with skewness boundary conditions at the interfaces, \(S\)-asymptotically periodic solutions for time-space fractional evolution equation, Robust error estimates for approximations of non-self-adjoint eigenvalue problems, Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations, On some fractional equations with convex-concave and logistic-type nonlinearities, Continuity properties of fractional powers, of the logarithm, and of holomorphic semigroups, Boundary values of holomorphic semigroups of unbounded operators and similarity of certain perturbations, Bifurcation points of Hammerstein equations, Regularized semigroups, iterated Cauchy problems and equipartition of energy, \(C\)-semigroups and strongly continuous semigroups, Some extension results for nonlocal operators and applications, A factorization of a quadratic pencils of accretive operators and applications, On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease, Semigroups of operators and second-order Cauchy problems, \(N\)-dimensional fractional Fokker-Planck equation and its solutions for anomalous radial two-phase flow in porous media, The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup, Second order incomplete expiring Cauchy problems, A direct approach to the weighted admissibility of observation operators for bounded analytic semigroups, n-th roots of a non-negative operator. Conditions for uniqueness, The time independent fractional Schrödinger equation with position-dependent mass, Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator, On spectral and fractional powers of damped wave equations, Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games, An invariant measure for the equation \(u_{tt}-u_{xx}+u^ 3=0\), On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients, Some inequalities for generalized commutators, A sufficient condition for the Carasso-Kato theorem, On the fractional integral of Weyl in \(L^ p\), The fractional porous medium equation on manifolds with conical singularities II, A rational preconditioner for multi-dimensional Riesz fractional diffusion equations, Chebyshev polynomials for higher order differential equations and fractional powers, The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence, A Gaussian method for the square root of accretive operators, Exponent Splitting Schemes for Evolution Equations with Fractional Powers of Operators, Function spaces via fractional Poisson kernel on Carnot groups and applications, Quantitative uniqueness for fractional heat type operators, A higher-order non-autonomous semilinear parabolic equation, Quantum fractional Ornstein-Uhlenbeck semigroups and associated potentials, Short-range scattering of Hartree type fractional NLS. II., Some properties of sub-Laplaceans, Differential Equations of Elliptic Type with Variable Operators and Homogeneous Robin Boundary Value Condition in UMD Spaces, A spectral approach to an integral equation, Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator, Extremal values of the (fractional) Weinstein functional on the hyperbolic space, Zur Charakterisierung von Ableitungen nichtganzer Ordnung im Rahmen der L<scp>APLACE</scp>‐Transformation, Unnamed Item, On fractional plasma problems, Abstract differential equations of elliptic type with general Robin boundary conditions in Hölder spaces, On semi-linear parabolic partial differential equations, Transmission problems in a thin layer set in the framework of the Hölder spaces: resolution and impedance concept, Fractional intertwinings between two Markov semigroups, Unnamed Item, An approximate representation of a solution to fractional elliptical BVP via solution of parabolic IVP, Feeling the heat in a group of Heisenberg type, A Remark on Cosine Families, A survey on numerical methods for spectral space-fractional diffusion problems, Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations, Representation of complex powers of C-sectorial operators, On the limiting behaviour of some nonlocal seminorms: a new phenomenon, Integral representation of solutions of semilinear elliptic equations in cylinders and applications, Definition of Physically Consistent Damping Laws with Fractional Derivatives, Fractional Laplacians : a short survey, Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions, Borderline gradient continuity for fractional heat type operators, A Quadrature Scheme for Steady-State Diffusion Equations Involving Fractional Power of Regularly Accretive Operator, Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons, Nonnegative solutions of a fractional differential inequality on Grushin spaces and nilpotent Lie groups, Ultraviolet-complete quantum field theories with fractional operators, On fractional powers of the Schrödinger operator with a potential singular on manifolds, Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity, Definition of Physically Consistent Damping Laws with Fractional Derivatives, Multilevel approximation of Gaussian random fields: Fast simulation, The associated operator Legendre function and the incomplete Cauchy problem, Study of boundary value and transmission problems governed by a class of variable operators verifying the Labbas-Terreni non commutativity assumption, An a posteriori error estimator for the spectral fractional power of the Laplacian, Sharp ultimate bounds of solutions to a class of second order linear evolution equations with bounded forcing term, SOME PROPERTIES OF OPERATOR EXPONENT, Some generalizations of Bessel and Flett potentials associated to the Laplace–Bessel differential operator, Unnamed Item, Multigrid Methods for Discrete Fractional Sobolev Spaces, Subordination principle for space-time fractional evolution equations and some applications, An Introduction to Fractional Powers of Quaternionic Operators and New Fractional Diffusion Processes, On the Decay Rate of the Singular Values of Bivariate Functions, Variable order subordination in the sense of Bochner and pseudo-differential operators, Unnamed Item, Complex powers of multivalued linear operatorswith polynomially bounded C-resolvent, Fractional powersof Bessel operator and its numerical calculation, The noncommutative fractional Fourier law in bounded and unbounded domains, On general Bitsadze-Samarskii problems of elliptic type in \(L^p\) cases, Cosine Families of Unbounded Operators, On Subordinated Holomorphic Semigroups, A Balakrishnan-Rubin type hypersingular integral operator and inversion of Flett potentials, Quantum scalar field theories with fractional operators, Pseudodifferential parabolic equations in uniform spaces, Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form, Fractional Powers of Momentum of a Spectral Distribution, Diagonalization of non-selfadjoint analytic semigroups and application to the shape memory alloys operator, Perturbation techniques in related differential equations, Compacité des résolvantes des opérateurs maximaux cycliquement monotones, Semilinear second order evolution equations of compact type with regular boundary conditions, Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times, Spaces of positive and negative frequency solutions of field equations in curved space–times. II. The massive vector field equations in static space–times, Schrödinger-type evolution equations in \(L^p(\Omega)\), On the axioms of scale space theory, Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space, Fractional powers of monotone operators in Hilbert spaces, An Agler-type model theorem forC₀-semigroups of Hilbert space contractions, Pseudoprocesses on a circle and related Poisson kernels, A direct approach to the Weiss conjecture for bounded analytic semigroups, Unnamed Item, Unnamed Item, Unnamed Item, Analytic domination by fractional powers of a positive operator, Ordinary differential equations in linear topological spaces. I, Ordinary differential equations in linear topological space. II, A note on linear hyperbolic evolution equations, A fractional PDE model for turbulent velocity fields near solid walls, Fractional powers of vector operators with first order boundary conditions, Familles résolvantes, générateurs, cogénérateurs, potentiels, The underdetermined Cauchy problem in Banach spaces, On sinc quadrature approximations of fractional powers of regularly accretive operators, Intégrales de résolvantes et calcul symbolique. (Integrals of resolvents and symbolic calculus.), Fractional thoughts, Fractional powers of operators and Riesz fractional integrals, Monotone iterative technique for time-space fractional diffusion equations involving delay, Resolution in hölder spaces of an elliptic problem in an unbounded domain, Totally Accretive Operators, The Harnack inequality for a class of nonlocal parabolic equations, On a class of functional–differential operators satisfying the Kato conjecture, A class of nonlocal hypoelliptic operators and their extensions, Numerical approximation of fractional powers of elliptic operators, A perturbation theorem for contraction semi-groups, Some uniqueness theorems for differential equations with operator coefficients, Semigroups of Unbounded Linear Operators in Banach Space, A perturbation theorem for semi-groups of linear operators, Representation of fractional powers of infinitesimal generators of semigroups, Fractional powers of higher-order vector operators on bounded and unbounded domains