Operational calculus

DOI10.1007/BF01377044zbMath0451.44003OpenAlexW4211012243MaRDI QIDQ1147936

V. S. Shishov, A. P. Prudnikov, Yu. A. Brychkov

Publication date: 1981

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01377044

zbMATH Keywords

bibliographyBibliographyMikusinski's operational calculusoperator differential equationsconvergence of operator seriesBessel- type operatorsgeneralized functions in operational calculusliterature on operational calculusmultidimensional operational calculus

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Calculus of Mikusi?ski and other operational calculi (44A40) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Bibliographies for mathematics in general (00A15) Research exposition (monographs, survey articles) pertaining to integral transforms (44-02)

Related Items (7)

Solving Prabhakar differential equations using Mikusiński's operational calculus ⋮ On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method ⋮ Stability and \(\psi\)-algebraic decay of the solution to \(\psi\)-fractional differential system ⋮ On Laplace transforms with respect to functions and their applications to fractional differential equations ⋮ An operational calculus approach to Hilfer-Prabhakar fractional derivatives ⋮ \(p\)-adic Mikusinski calculus and its applications to the Fourier and the Mahler expansions of locally constant functions ⋮ Horizontal collaboration in freight transport: concepts, benefits and environmental challenges

Cites Work

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• The multiplier problem
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• Operator homomorphisms
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• The Mikusinski Operators as a Topological Space
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• Übertragung der P<scp>OST</scp>‐W<scp>IDDER</scp>schen Umkehrformel der Laplace‐Transformation auf die ℒ‐Transformation
• Operatorenrechnung für Funktionen einer stetigen und einer diskreten Variablen
• Funktionentheoretische Untersuchungen im M<scp>IKUSIŃSKI</scp>schen Operatorenkörper
• Titchmarsh's Theorem for Analytic Functions
• Bemerkungen zur "algebraischen" Exponentialfunktion im Mikusiński'schen Operatorenkörper
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• Laplace Transformations of Distributions
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• Bemerkungen zur Meijer‐Transformation und Anwendungen
• Differentiationssätze der ℒ‐Transformation und Differentialgleichungen nach dem Operator \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{d}{dt} t^{\frac{1}{n}-v} \left( t^ {1-\frac{1}{n}} \frac{d}{dt}\right)^{n-1} t^{v+1-\frac{2}{n}} $\end{document}
• Remark on Certain Convolution Transforms
• Zur funktionentheoretischen Auffassung der MIKUSIŃSKISchen Operatorenrechnung
• An Operational Method in Partial Differential Equations
• Zum Problem der Operatorfunktionen mit verschwindender Ableitung
• The Convolution Integral
• On Operators and Distributions
• On approximate solutions to the convolution equation on the half-line
• A Division Algebra for Sequences and Its Associated Operational Calculus
• The Convolution Ring of Sequences
• Operators of discrete analytic functions
• Operators of discrete analytic functions and their application
• Iterative Berechnung der <scp>Tschebyscheff</scp>schen Alternante für quadratische Polynome
• Some Operational Formulas
• Complex Number Algebra as a Simple Case of Heaviside Operational Calculus
• A Representation of Linear Continuous Operators on Testing Functions and Distributions
• Inversion of a Convolution Transform Related to Heat Conduction
• On continuous endomorphisms of Mikusinski's operator field
• Eine nichtkommutative Operatorenrechnung und ihre Anwendung auf Differentialgleichungen der Physik
• An algebraic view of distributions and operators
• An algebra of generalized functions on an open interval; two-sided operational calculus
• Quasi-Inverses of Sequences
• A Survey of the Development of Operational Calculus
• Asymptotische Einschließung von Lösungen expliziter Operatordifferentialgleichungen
• Linear operators and operational calculus. Part I
• Generalized Translations Associated with a Differential Operator
• Asymptotic Inversion of Laplace Transforms: A Class of Counterexamples
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• Operants: A Functional Calculus for Non-Commuting Operators
• On power series in the differentiation operator
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• Linear Equations with an Operator Polynomial on the Left Side
• Algebraic theory of right invertible operators
• An Application of the Generating Function to Differential Equations
• Asymptotische Auffassung der Operatorenrechnung
• Continuity and Perfect Operators

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