Convolution operators on some spaces of functions and distributions in the theory of circuits

Borys, Andrzej; Kamiński, Andrzej; Sorek, Sławomir

dc.contributor.author	Borys, Andrzej
dc.contributor.author	Kamiński, Andrzej
dc.contributor.author	Sorek, Sławomir
dc.contributor.editor	Hejduk, Jacek
dc.contributor.editor	Kowalczyk, Stanisław
dc.contributor.editor	Pawlak, Ryszard J.
dc.contributor.editor	Turowska, Małgorzata
dc.date.accessioned	2018-05-11T10:14:46Z
dc.date.available	2018-05-11T10:14:46Z
dc.date.issued	2015
dc.identifier.citation	Borys A., Kamiński A., Sorek S., Convolution operators on some spaces of functions and distributions in the theory of circuits, [w:] Modern Real Analysis, J. Hejduk, St. Kowalczyk, R.J. Pawlak, M. Turowska (red.), WUŁ, Łódź 2015, doi: 10.18778/7969-663-5.03.	pl_PL
dc.identifier.isbn	978-83-7969-663-5
dc.identifier.uri	http://hdl.handle.net/11089/24743
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Modern Real Analysis;
dc.rights	Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/pl/	*
dc.subject	linear circuit	pl_PL
dc.subject	nonlinear circuit	pl_PL
dc.subject	Taylor series	pl_PL
dc.subject	Volterra series	pl_PL
dc.subject	(neutrix) product of distributions	pl_PL
dc.subject	(neutrix) kth power of a distribution	pl_PL
dc.title	Convolution operators on some spaces of functions and distributions in the theory of circuits	pl_PL
dc.type	Book chapter	pl_PL
dc.rights.holder	© Copyright by Authors, Łódź 2015; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2015	pl_PL
dc.page.number	27-43	pl_PL
dc.contributor.authorAffiliation	Gdynia Maritime University, Faculty of Electrical Engineering	pl_PL
dc.contributor.authorAffiliation	University of Rzeszów, Faculty of Mathematics and Natural Sciences	pl_PL
dc.contributor.authorAffiliation	University of Rzeszów, Faculty of Mathematics and Natural Sciences	pl_PL
dc.identifier.eisbn	978-83-7969-955-1
dc.references	P. Antosik, J. Mikusiński and R. Sikorski, Theory of Distributions. The Sequential Approach, Elsevier-PWN, Amsterdam-Warszawa, 1973.	pl_PL
dc.references	E. Bedrosian and S. O. Rice, The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs, Proceedings of the IEEE 59 (1971), 1688-1707.	pl_PL
dc.references	A. Borys, Consideration of Volterra series with excitation and/or impulse responses in the form of Dirac impulses, IEEE Transactions on Circuits and Systems II 57 (2010), 466-470.	pl_PL
dc.references	A. Borys, A. Kamiński and S. Sorek, Volterra systems and powers of Dirac delta impulses, Integral Transforms Spec. Func. 20 (2009), 301-308.	pl_PL
dc.references	A. Borys and W. Sieńko, Volterra series and multiplication of Dirac impulses, presentation by the first author at the conference ’Linear and Non-linear Theory of Generalized Functions’, Będlewo, 2007.	pl_PL
dc.references	J. F. Colombeau, New Generalized Functions and Multiplication of Distributions, North Holland, Amsterdam, New York, Oxford, 1984.	pl_PL
dc.references	J. G. van der Corput, Introduction to the neutrix calculus, J. Analyse Math. 7 (1959/60), 281-398.	pl_PL
dc.references	B. Fisher, The product of distributions, Quart. J. Math. Oxford 22 (2) (1971), 291- 298.	pl_PL
dc.references	N. J. Fliege, Systemtheorie, Teubner, Stuttgart, 1991.	pl_PL
dc.references	E. G. Gilbert, Functional expansions for the response of nonlinear differential systems, IEEE Transactions on Automatic Control 22 (6) (1977), 909-921.	pl_PL
dc.references	S. Haykin and B. Van Veen, Signals and Systems, Wiley, New York, 2003.	pl_PL
dc.references	J. Horváth, Topological Vector Spaces and Distributions, Vol. 1, Addison-Wesley, Reading, 1966.	pl_PL
dc.references	A. Kamiński, Remarks on delta- and unit-sequences, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 26 (1978), 25-35.	pl_PL
dc.references	A. Kamiński, On model delta-sequences and the product of distributions, in Complex Analysis and Generalized Functions, I. Dimovski, V. Hristov, eds., Varna, 15–21 September 1991, 148-155.	pl_PL
dc.references	A. Kamiński and S. Sorek, Linear and nonlinear systems and neutrix powers of Dirac delta impulses, presentation by the second author at the 28th International Conference on Real Functions Theory, Stará Lesná, 2014.	pl_PL
dc.references	E. L. Koh and C. K. Li, On the distributions dk and (dt)k, Math. Nachr. 157 (1992), 243-248.	pl_PL
dc.references	J. Mikusiński, Criteria of the existence and of the associativity of the product of distributions, Studia Math. 21 (1962), 253-259.	pl_PL
dc.references	J. Mikusiński, On the square of the Dirac delta-distribution, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 14 (1966), 511-513.	pl_PL
dc.references	M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Longman, New York, 1992.	pl_PL
dc.references	L. Schwartz, Théorie des Distributions vols. I-II, Hermann, Paris, 1950-1951.	pl_PL
dc.references	S. Sorek, On the notion of neutrix in the theory of generalized functions, in preparation.	pl_PL
dc.references	B. Fisher, The neutrix distribution product xr + d(r1)(x), Studia Sci. Math. Hungar. 9 (1974), 439-441.	pl_PL
dc.identifier.doi	10.18778/7969-663-5.03