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Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators
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This reprint contains a collection of research papers on spectral theory for differential and functional differential operators. Spectral theory plays a fundamental role in mathematics and has applications in various fields of science and engineering, e.g., in quantum and classical mechanics, geophysics, acoustics, and electronics. The collection includes recent studies on a variety of topics such as analytical and numerical methods for solving direct and inverse spectral problems, new developments in the theory of partial differential equations, pseudo-differential equations with fractional derivatives, asymptotical analysis for solutions of differential equations, spectral theory for abstract operators in Hilbert spaces, and inverse nodal problems.
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Keywords
- Abel–Lidskii basis property
- acoustic equation
- asymptotic methods
- Bessel Functions
- Blow-up
- boundary value problem
- Campbell’s identity
- Cauchy problem
- Chebyshev wavelet
- coercive quasilinear inequalities
- completely monotonic functions
- constant delay
- constructive solution
- convergence exponent
- convergence rate
- convolution operator
- counting function
- Differences
- differential operators on graphs
- differential pencils
- direct methods
- direct scattering problem
- distributed fractional derivative
- distribution coefficients
- emerging eigenvalues
- existence
- fixed point theorem
- Fox H-function
- fractional differential equation
- fractional integrals and derivatives
- frozen argument
- functional-differential operator
- Gelfand–Levitan–Krein–Marchenko equation
- Graph
- half-inverse problem
- higher-order differential operators
- Hochstadt-Lieberman problem
- initial boundary value problem
- initial function
- Integral equations
- inverse coefficient problem
- inverse nodal problem
- inverse problems
- inverse scattering problem
- inverse spectral problem
- inverse spectral problems
- Ionkin condition
- Jost solution
- KPZ nonlinearities
- Melling transform
- method of spectral mappings
- multi-dimensional integral transform
- non-selfadjoint Schrödinger operator
- norm resolvent convergence
- Orthogonal polynomials
- oscillating coefficients
- paired-dense nodal subset
- partial inverse nodal problem
- partial inverse spectral problem
- perturbation
- point interaction
- potential
- potential function
- quasi-derivatives
- quasiliner equation
- regular solutions
- regularized trace formulae
- Robin condition
- Schatten–von Neumann class
- Shin–Zettl matrix
- singular differential equations of odd order
- small cavity
- spatial nonlocal problems
- spectrum
- splitting method
- strictly accretive operator
- Sturm-Liouville operator
- Sturm–Liouville equations
- Sturm–Liouville-type operator
- thema EDItEUR::U Computing and Information Technology
- thema EDItEUR::U Computing and Information Technology::UY Computer science
- Uniqueness
- weighted space
- zeros
Links
DOI: 10.3390/books978-3-7258-1596-8Editions