Non-Euclidean functional analysis and electronics

DOI10.1090/S0273-0979-1982-15001-7zbMath0493.46047MaRDI QIDQ3955921

J. William Helton

Publication date: 1982

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

interpolation theorycircuits with prescribed power gain

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Analytic circuit theory (94C05) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Linear operators on function spaces (general) (47B38) Moment problems and interpolation problems in the complex plane (30E05) Structure theory of linear operators (47A65) Representations of Lie and linear algebraic groups over local fields (22E50) Canonical models for contractions and nonselfadjoint linear operators (47A45) Linear operators on spaces with an indefinite metric (47B50)

Related Items (18)

A Lie-theoretic setting for the classical interpolation theories ⋮ Patterns and structure in systems governed by linear second-order differential equations ⋮ Gamma-generating matrices, j-inner matrix function and related extrapolation problems. I ⋮ Qualitative properties of solutions to \(H^{\infty}\)-optimization problems ⋮ Generalized interpolation in control theory ⋮ Regular and singular J-inner matrix-functions and the corresponding interpolation problems ⋮ Characterizing optimal multiport matching transformers ⋮ \(H^\infty\) approximation with point constraints applied to impedance estimation ⋮ Control systems and number theory ⋮ Möbius deconvolution on the hyperbolic plane with application to impedance density estimation ⋮ The rational approximation of circuit design ⋮ Cascade equivalence of linear systems ⋮ Applications of Pick-Nevanlinna interpolation theory to retention- solubility studies in the lungs ⋮ Noneuclidean harmonic analysis, the central limit theorem, and long transmission lines with random inhomogeneities ⋮ A family of domains associated with \(\mu\)-synthesis ⋮ On the Hankel-norm approximation of upper-triangular operators and matrices ⋮ Robust stabilization of distributed systems ⋮ A bang-bang theorem for optimization over spaces of analytic functions

Cites Work

• Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions
• Applications of Pick-Nevanlinna interpolation theory to retention- solubility studies in the lungs
• An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types. II
• The distance of a function to \(H^\infty\) in the Poincaré metric; electrical power transfer
• Factorization results related to shifts in an indefinite metric
• Lifting commuting operators
• Interpolation with positive-real functions
• Systems of integral equations on a half line with kernels depending on the difference of arguments
• On a Certain Linear Fractional Transformation
• Feedback, minimax sensitivity, and optimal robustness
• Broadbanding:Gain equalization directly from data
• On the minimal spectral factorization of nonsingular positive rational matrices
• On the irreducible cascade synthesis of a system with a real rational transfer matrix
• On Hankel Operator Ranges, Meromorphic Pseudo-Continuations and Factorization of Operator-Valued Analytic Functions^†
• Subinvariants for Analytic Mappings on Matrix Balls
• Generalized Interpolation in H ∞
• On the Spectra of Bounded, Hermitian, Hankel Matrices
• Best uniform approximations via annihilating measures
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
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