The \({\mathcal L}^ p\) space of a positive definite matrix of measures and density of matrix polynomials in \({\mathcal L}^ 1\)

DOI10.1006/jath.1996.3073zbMath0886.46029OpenAlexW2064592613MaRDI QIDQ1365565

Pedro Lopez-Rodriguez, Antonio J. Duran

Publication date: 4 September 1997

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1996.3073

zbMATH Keywords

momentsdensitycompact in the vague topologypositive definite matrices of measures

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of measures (46E27)

Related Items (8)

Interpolation with symmetry and a Herglotz theorem in the bicomplex setting ⋮ On Optimal Transport of Matrix-Valued Measures ⋮ Doubly invariant submodules in \(L^{\alpha }\)-spaces ⋮ The Schrödinger problem on the non-commutative Fisher-Rao space ⋮ Density of systems of trigonometric polynomials in \(L^p\), \(0<p<1\) ⋮ Representation of the trilinear form associated with orthogonal matrix polynomials ⋮ Measurable diagonalization of positive definite matrices ⋮ \(N\)-extremal matrices of measures for an indeterminate matrix moment problem

Cites Work

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• Density questions in the classical theory of moments
• Polynomial interpolation and Gaussian quadrature for matrix-valued functions
• Matrix inner product having a matrix symmetric second-order differential operator
• Scattering theory and matrix orthogonal polynomials on the real line
• Orthogonal matrix polynomials and higher-order recurrence relations
• Orthogonal matrix polynomials: zeros and Blumenthal's theorem
• A generalization of Favard's theorem for polynomials satisfying a recurrence relation
• The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measure
• Markov's Theorem for Orthogonal Matrix Polynomials
• Inclusion Relations for SomeLp-Spaces of Operator-Valued Functions
• Some approximation problems in $L^{p}$-spaces of matrix-valued functions
• Density Questions for the Truncated Matrix Moment Problem
• On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

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