On the Elementary Retarded, Ultrahyperbolic Solution of the Klein-Gordon Operator, Iterated k Times
Let t = (t1,...,tn) be a point of ℝn. We shall write . We put, by the definition, Wα(u, m) = (m-2u)(α - n)/4[π(n - 2)/22(α + n - 2)/2G{cyrillic}(α/2)]J(α - n)/2(m2u)1/2; here α is a complex parameter, m a real nonnegative number, and n the dimension of the space. Wα(u, m), which is an ordinary funct...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Blackwell Publishing Ltd
1988
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
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| 008 | 190411s1988 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84954428232 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Trione, S.E. | |
| 245 | 1 | 3 | |a On the Elementary Retarded, Ultrahyperbolic Solution of the Klein-Gordon Operator, Iterated k Times |
| 260 | |b Blackwell Publishing Ltd |c 1988 | ||
| 270 | 1 | 0 | |m Trione, S.E.; Departmento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresArgentina |
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a Let t = (t1,...,tn) be a point of ℝn. We shall write . We put, by the definition, Wα(u, m) = (m-2u)(α - n)/4[π(n - 2)/22(α + n - 2)/2G{cyrillic}(α/2)]J(α - n)/2(m2u)1/2; here α is a complex parameter, m a real nonnegative number, and n the dimension of the space. Wα(u, m), which is an ordinary function if Re α ≥ n, is an entire distributional function of α. First we evaluate (□ + m2)Wα + 2(u, m) = Wα(u, m), where (□ + m2) is the ultrahyperbolic operator. Then we express Wα(u, m) as a linear combination of Rα(u) of differntial orders; Rα(u) is Marcel Riesz's ultrahyperbolic kernel. We also obtain the following results: W-2k(u, m) = (□ + m2)kδ, k = 0, 1,...; W0(u, m) = δ; and (□ + m2)kW2k(u, m) = δ. Finally we prove that Wα(u, m = 0) = Rα(u). Several of these results, in the particular case μ = 1, were proved earlier by a completely different method. © 2015 Wiley Periodicals, Inc., A Wiley Company. |l eng | |
| 593 | |a Departmento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina | ||
| 773 | 0 | |d Blackwell Publishing Ltd, 1988 |g v. 79 |h pp. 127-141 |k n. 2 |p Stud. Appl. Math. |x 00222526 |w (AR-BaUEN)CENRE-6932 |t Studies in Applied Mathematics | |
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| 856 | 4 | 0 | |u https://doi.org/10.1002/sapm1988792127 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00222526_v79_n2_p127_Trione |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222526_v79_n2_p127_Trione |y Registro en la Biblioteca Digital |
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| 999 | |c 72958 | ||