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Displaying 41 – 60 of 92

Linear distributional differential equations of the second order

Milan Tvrdý (1994)

Mathematica Bohemica

The paper deals with the linear differential equation (0.1) ${(p u^{'})}^{'} + q^{'} u = f^{''}$ with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

New generalized functions. Multiplication of distributions. Physical applications. Contribution of J. Sebastião e Silva

Colombeau, J.F. (1982)

Portugaliae mathematica

Non-Standard Analysis And Generalized Functions.

Steven M. Moore (1980)

Revista colombiana de matematicas

Nové výsledky v theorii distribucí

J. Mikusiński (1957)

Pokroky matematiky, fyziky a astronomie

On alternative functional equations. (Short Communication).

Halina Swiatak (1976)

Aequationes mathematicae

On representation of temperate distributions

Jan Kučera (1972)

Czechoslovak Mathematical Journal

On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra

Jan Ligęza (1996)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On vector measures and distributions

Miloslav Duchoň (1989)

Mathematica Slovaca

One-parameter semigroups in the convolution algebra of rapidly decreasing distributions

(2012)

Colloquium Mathematicae

The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $_{C}^{'} (ℝ ⁿ; M_{m \times m})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G \in_{C}^{'} (ℝ ⁿ; M_{m \times m})$ is the generating distribution of an i.d.c.s. if and only if the operator $\partial_{t} \otimes_{m \times m} - G *$ on $ℝ^{1 + n}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.