Patterns and structure in systems governed by linear second-order differential equations

DOI10.1007/BF00046724zbMath0621.34001OpenAlexW2094324873MaRDI QIDQ1089815

Robert W. Carroll

Publication date: 1986

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00046724

zbMATH Keywords

generating functionsfilteringscattering theoryToeplitz operatorsWiener-Hopf equationsgeneralized convolutionrandom evolutionstransmutationPaley-Wiener theoryBergman-Gilbert operatorDarboux-Christoffel formulasdeBranges spacesKontorovič-Lebedev inversionlinear second order differential operatorsParseval formulasWeyl integrals

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Estimation and detection in stochastic control theory (93E10) Theoretical approximation of solutions to ordinary differential equations (34A45) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Inverse problems involving ordinary differential equations (34A55) Ordinary differential operators (34L99) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items (1)

Some features of the maps from potential to spectral data

Cites Work

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• Transmutation theory for certain radial operators
• Hilbert spaces of analytic functions, inverse scattering and operator models. I
• Impedance profile inversion via the first transport equation
• Some remarks on the generalized Gelfand-Levitan equation
• Equisummability of eigenfunction expansions under analytic multipliers
• The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
• The inversion of acoustical impedance profile by methods of characteristics
• The Gelfand-Levitan and Marčenko equations via transmutation
• Constructive methods for elliptic equations
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Random evolutions: A survey of results and problems
• About the stability of the inverse problem in 1-D wave equations application to the interpretation of seismic profiles
• Integral representations for Jacobi polynomials and some applications
• A class of orthogonal polynomials
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• The convolution structure for Jacobi function expansions
• Discrete and continuous boundary problems
• THE CONSTRUCTION OF SOLUTIONS TO ACOUSTIC SCATTERING PROBLEMS IN A SPHERICALLY STRATIFIED MEDIUM
• The determination of the scattering potential from the spectral measure function
• Generating Functions for Hermite Functions
• Introduction to complex orbital momenta
• Integral Operators in the Theory of Linear Partial Differential Equations
• A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources
• The One-Dimensional Inverse Problem of Reflection Seismology
• Partial differential equation techniques in transmutation
• Transmutation and linear stochastic estimation
• Impedance profile recovery from transmission data
• Une Transformation de Laplace–Jacobi
• Un a iransform theory involving whittaker functions
• Transmutation via the momentum plane
• Differential Methods in Inverse Scattering
• Fourier type analysis and the marcenko equation
• Some Remarks on a Canonical Marcenko Equation
• Some spectral formulas for systems and transmission lines
• Spectral and scattering inverse problems
• The Factorization and Representation of Operators in the Algebra Generated by Toeplitz Operators
• Scattering theory and polynomials orthogonal on the unit circle
• Scattering theory for automorphic functions
• The Kontorovich-Lebedev Transform
• On the and Transformations
• Scattering techniques for a one dimensional inverse problem in geophysics
• Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium
• Some Remarks on singular pseudodifferential operators
• Non-Euclidean functional analysis and electronics
• Stability for the one dimensional inverse problem via the gel’fand-levitan equation
• Research announcement
• On complete recovery of geophysical data
• The Riemann—Liouville Integral and Parameter Shifting in a Class of Linear Abstract Cauchy Problems
• Inverses of Toeplitz Operators, Innovations, and Orthogonal Polynomials
• Transmutation and separation of variables
• On the ranges of certain fractional integrals II†
• Two-Dimensional Random Fields and Representation of Images
• On the asymptotic behavior of the spectral function of a self adjoint second order differential equation
• On the inversion problem in the λ-plane
• On the inversion problem in the λ-plane.—II
• A Modification of Hilbert Transforms, the Weyl Integral and Functional Equations
• Related Partial Differential Equations and their Applications
• On a Modification of the Hilbert Transform
• Analytic Properties of a Class of Potentials and the Corresponding Jost Functions
• Differential equations in which the Poisson process plays a role
• Complex Angular Momenta in Potential Scattering
• On a Factor Automorphism of a Normal Dynamical System
• Application of a Resolvent Identity to a Linear Smoothing Problem
• The Construction of Solutions for Boundary Value Problems by Function Theoretic Methods
• Generalized Translations Associated with a Differential Operator
• On the Ranges of Certain Fractional Integrals
• A Note on Least Squares Estimation by the Innovations Method
• Generalized axially symmetric potential theory
• The singular solutions and the cauchy problem for generalized Tricomi equations

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