Distributions and Their Hermite Expansions

DOI10.1063/1.1665472zbMath0205.12901OpenAlexW2068856917MaRDI QIDQ5604720

Publication date: 1971

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1665472

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Applications of functional analysis in quantum physics (46N50) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (51)

Nuclear space facts, strange and plain ⋮ A differential structure for quantum mechanics ⋮ Mehler kernel approach to tempered distributions ⋮ Frames, Semi-Frames, and Hilbert Scales ⋮ Generalized functions and Laguerre expansions ⋮ The partial inner product space method: a quick overview ⋮ Tempered generalized functions and Hermite expansions ⋮ On the duality of regular and local functions ⋮ The Hermite expansion of the characteristic functions ⋮ Homotopy Transfer and Effective Field Theory I: Tree‐level ⋮ On eigenmeasures under Fourier transform ⋮ A Feynman–Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise ⋮ Probabilistic aspects of quantum field theory ⋮ Noncommutative quantum decomposition of Gegenbauer white noise process ⋮ Large deviation principle for the field in prequantum classical statistical field theory ⋮ A dimensionally continued Poisson summation formula ⋮ Stochastic Clairaut equation on algebra of generalized functions ⋮ The problem of moments in the phase-space formulation of quantum mechanics ⋮ TV-based reconstruction of periodic functions ⋮ Algebras of distributions suitable for phase-space quantum mechanics. I ⋮ An analytic characterization of \((p,q)\)-white noise functionals ⋮ Some comments on rigorous finite-volume Euclidean quantum field path integrals in the analytical regularization scheme ⋮ Hermite expansions of some tempered distributions ⋮ Partial Inner Product Spaces, a Unifying Language for Quantum Mechanics ⋮ Continuity of affine transformations of white noise test functionals and applications ⋮ Multidimensional Lévy white noise in weighted Besov spaces ⋮ Kernel theorems for the spaces of tempered ultradistributions ⋮ On differential operators in white noise analysis ⋮ Axioms for Euclidean Green's functions. II ⋮ A Characterization of White Noise Test Functionals ⋮ A class of generalized Lévy Laplacians in infinite dimensional calculus ⋮ Partial inner product spaces. I: General properties ⋮ An algebra of pseudodifferential operators and the asymptotics of quantum mechanics ⋮ Structural theorems for Gelfand–Shilov spaces ⋮ EXAMPLES OF DERIVATION-BASED DIFFERENTIAL CALCULI RELATED TO NONCOMMUTATIVE GAUGE THEORIES ⋮ Wavelet analysis of the Besov regularity of Lévy white noise ⋮ The \(n\)-term approximation of periodic generalized Lévy processes ⋮ Localization of Fréchet frames and expansion of generalized functions ⋮ Fractional transformations of generalized functions ⋮ A weighted occupation time for a class of measure-valued branching processes ⋮ Self-adjoint algebras of unbounded operators ⋮ Towards three-dimensional conformal probability ⋮ Stochastic quantization using a kerneled Langevin equation ⋮ Essential self-adjointness of Schrödinger operators with positive potentials ⋮ On the directional dependence of composite field operators ⋮ L-BMO bounds for pseudo-multipliers associated with the harmonic oscillator ⋮ Multikernel Regression with Sparsity Constraint ⋮ The Hermite function expansions of the Heaviside function ⋮ Hilbert space for quantum mechanics on superspace ⋮ The Schwartz space: tools for quantum mechanics and infinite dimensional analysis ⋮ A characterization of the generalized functions via the special Hermite expansions

Cites Work

This page was built for publication: Distributions and Their Hermite Expansions