Results 21 to 30 of about 160 (136)
A Generalization of the Mikusinski Operational Calculus [PDF]
Proceedings of the American Mathematical Society, 1968 0. Introduction. In his version of the operational calculus Mikusinski uses as a starting point the familiar theorem from algebra tlhat every integral domain can be embedded isomorphically in a field. He shows that the class of complex-valued continuous functions defined on [0, cO) forms an integral domain when addition and multiplication are taken to ...
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International Journal of Mathematics and Mathematical Sciences, 2000 The construction of Boehmians on a manifold requires a commutative convolution structure. We present such constructions in two specific cases: an N-dimensional torus and an N-dimensional sphere. Then we formulate conditions under which a construction of
Piotr Mikusiński
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Operational calculus and differential equations with infinitely smooth coefficients
International Journal of Mathematics and Mathematical Sciences, 1990 A subring MF of the field of Mikusiński operators is constructed as a countable union space. Some topological properties of MF are investigated. Then, the product of an infinitely differentiable function and an element of MF is given and is used to ...
Dennis Nemzer
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On Antosik’s Lemma and the Antosik-Mikusinski Basic Matrix Theorem [PDF]
Proceedings of the American Mathematical Society, 2002 The Antosik-Mikusinski theorem states the following. Let \(G\) be an abelian topological group, \(x_{ij} \in G\) for \(i, j \in \mathbb{N}\). If \(\lim_i x_{ij}\) exists for each \(j\) and, for each strictly increasing sequence of positive integers \(\{m_j\}\) there is a subsequence \(\{n_j\}\) such that \(\{\sum_jx_{in_j}\}\) is a Cauchy sequence ...
Qu, Wenbo, Wu, Junde
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A Noncommutative Mikusinski Calculus
, 2012 We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the differential algebra underlying the given ring of boundary problems.
Rosenkranz, Markus, Korporal, Anja
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On the Fourier transform and the exchange property
International Journal of Mathematics and Mathematical Sciences, 2005 A simplified construction of tempered Boehmians is presented. The new construction shows that considering delta sequences and convergence arguments is not essential.
Dragu Atanasiu, Piotr Mikusiński
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The support of Mikusiński operators [PDF]
Transactions of the American Mathematical Society, 1973 A class of Mikusiriski operators, called regular operators, is studied. The class of regular operators is strictly smaller than the class of all operators, and strictly larger than the class of all distributions with left bounded support. Regular operators have local properties.
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Convergence semigroup categories
Applied General Topology, 2013 Properties of the category consisting of all objects of the form (X, S, λ) are investigated, where X is a convergence space, S is a commutative semigroup, and λ: X × S → X is a continuous action. A “generalized quotient” of each object is defined without
Gary Richardson +2 more
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On the topology of generalized quotients
Applied General Topology, 2008 Generalized quotients are defined as equivalence classes of pairs (x, f), where x is an element of a nonempty set X and f is an element of a commutative semigroup G acting on X.
Józef Burzyk +2 more
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Responses of African Savanna Trees to Large Herbivore Extinction and Rewilding
Ecology Letters, Volume 29, Issue 3, March 2026.Trophic rewilding may be a restoration ‘win‐win’ if the return of extirpated wildlife also restores lost ecosystem function, but few studies have addressed whether wildlife reintroduction is capable of reversing changes that occurred during extirpation.
Tyler C. Coverdale +5 more
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