In this article, we introduce the distributional family B�+mn n(V ) defined by (3). Bmn n(V ) is ... more In this article, we introduce the distributional family B�+mn n(V ) defined by (3). Bmn n(V ) is a generalization of distributional family R�(u) defined by (6), due to Y. Nozaki and this is called in (2) the Marcel Riesz Ultrahyperbolic Kernel. We obtain the formula L k {B�+mn n(V )} = C�,m,nB�+mn n 2km(V ) and evaluate B�+mn n(V ) at � = −2m( n + k − n 2m ) for the cases: µ = 2ms + m,
En este articulo se introduce la familia de funciones distribucionales ( ) 2 B x definida en ... more En este articulo se introduce la familia de funciones distribucionales ( ) 2 B x definida en (1) y usando laTransformada de Fourier se obtienen propiedades para los casos 0, 2k y 2k,k 1,2,... Usando la Transformada de Fourier, ( ) 2 B x puede ser expresada como combinacion lineal de y sus derivadas (ver, formula (27) y le damos un sentido a la propiedad ( ) ( ) 2 2 B x B x (ver, formula (44)) donde el simbolo significa convolucion. En la formula (33) aparece una nueva expresion para la delta de Dirac (x). Por otra parte, se introduce la familia de funciones distribucionales ( ) 2 M x definida en (54) y para 2k,E (x) k (ver, formula (62)) es solucion elemental del operador 2 2 1 dx d iterado k -veces
Sea M=M(x_1,…x_n ) una forma cuadratica definida en (18), en este articulo se define la distribuc... more Sea M=M(x_1,…x_n ) una forma cuadratica definida en (18), en este articulo se define la distribucion (M±i0)^λy se encuentra el residuo en λ=-n/2m-k/m m=1,2,…y k=0,1,2,… como consecuencia se obtiene la propiedad F_(-2km)^±=L_a^k {δ(x)} (ver formula (42)), donde F_α^± es la familia de funciones distribucionales definida por (35) y L_a^k es el operador definido por (39) y δ(x) es la distribucion delta de Dirac. Finalmente usando la transformada de Fourier de F_α^± se le da un sentido al producto de convolucion L_a^k {δ(x)}*L_a^l {δ(x)} (ver formula (59). Los resultados obtenidos en este articulo son generalizaciones de formulas que aparecen en ([1], pagina 353, ([2])) y ([3]) pagina 346, formula 5.4. Clasificacion segun AMS: 46F10 Palabras Claves: Distribucion; Residuo; Transformada de Fourier.
RESUMEN Sea P Px 1 ,. .. . , x n una forma cuadrática en n variables definida por (1) y sea ... more RESUMEN Sea P Px 1 ,. .. . , x n una forma cuadrática en n variables definida por (1) y sea P la distribución definida por (3) donde es un número complejo. Usando el desarrollo en serie de Laurent de P y considerando las signaturas p, q de Px, damos un sentido a los productos distribucionales P l .
In this note we give a sense to certain kinds of n‐dimensional distributional Hankel transforms o... more In this note we give a sense to certain kinds of n‐dimensional distributional Hankel transforms of the Dirac measure δ(k)(m2 + P). The most important result is the interchange formula between the product and the convolution of the Hankel transform of δ(k)(m2 + P).
In this paper we generalize the result obtained by Gonzáles Domínguez, Scarfiello and Fisher (A. ... more In this paper we generalize the result obtained by Gonzáles Domínguez, Scarfiello and Fisher (A. Gonzáles Domínguez and R. Scarfiello, Rev. Un. Mat. Argentina, Volumen de Homenaje a Beppo Levi (1956) 58–67; B. Fisher, Proc. Cambridge Philos. Soc. 72 (1972) 201–204). This result can be used in quantum field theory for the evaluation of products of propagators of the fields.
Journal of Mathematical Chemistry - J MATH CHEM, 2000
In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\d... more In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta ^{(k - 1)} (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}$$ and $$\delta ^{(k - 1)} (x_0 - \left| x \right|) \cdot \delta ^{(k - 1)} (x_0 + \left| x \right|)$$ . The first of them is a generalization of the product $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}{\text{ }}$$ given in [1, p. 158].
The present note contains the Tables of Fourier, Laplace and Hankel transforms of several dimensi... more The present note contains the Tables of Fourier, Laplace and Hankel transforms of several dimensional generalized functions. They are, mainly, based on the Laplace transform of retarded, Lorentz-invariant functions and the Fourier transforms of causal distributions.
In our former paper, [1], we have obtained an expansion for ([1], [pp. 123-125]), considering the... more In our former paper, [1], we have obtained an expansion for ([1], [pp. 123-125]), considering the cases n odd and n even separately. In the case n even, the formula obtained is under the conditions . The case was not studied. The main purpose of this paper is to extend the formula (∗) for considering two posibilities: a) p and q even; b) p and q odd.
Let P(x) be a quadratic form defined by (1).We know from(Gelfand and Shilov 1964)) that the equat... more Let P(x) be a quadratic form defined by (1).We know from(Gelfand and Shilov 1964)) that the equation {u(1 , 2 ,. .)} =f(x1,...xn) is often called ultrahyperbolic, where P=P(x) is defined by(31)and by (5). In this article we give a sense the elementary solution of the equation {u(1 , 2 ,. .)} =f(x1,...xn) where is the operator L{P} iterated m-times. {u(1 , 2 ,. .)} =f(x1,...xn
In this note we establish the distributional eonvolution produets of the form (P ± iD)> '... more In this note we establish the distributional eonvolution produets of the form (P ± iD)> ' * c5(Io} (p+) (e.E. (1,2,12), (1,1,40), (1, 1,41), (1, 1,42) and (1,1,43)) and (m2 + P ± iD)> ' * c5(Io} (m2 + P) (e.E. (1,3,4), (1,3,5), (1,3,6), (1,3, 7) and (1,3,8)). We obtain the results by using systematieally the Fourier transformation and to obtain (m2 + P ± iD)a-l * c5(Io} (m2 + P) we have employ the expansion c5(Io} (m2 + P) = L: (:2r c5(Io+JI}(P+) JI?:,:o (e.E. [2] , page 6, formula (1, 1,24)). The eonvolution produet (P ± iD)> ' * c5(Io} (p+) generalizes the result ([1] , page 13, formula (1,3,6)).
En este artículo se le dio un sentido al producto de convolución de δ (k-1)(1- x2)∗δ (l-1) (1- x2... more En este artículo se le dio un sentido al producto de convolución de δ (k-1)(1- x2)∗δ (l-1) (1- x2). Como caso particular se obtuvo una fórmula del producto de convolución de δ (1- x2)∗δ (1- x2) (C.f. fórmula (38)). Palabras Claves: Convolución; ProductoDOI: http://dx.doi.org/10.5377/nexo.v22i2.45Nexo Revista Científica Vol. 22, No. 02, pp.66-71/Diciembre 2009
In this article, we introduce the distributional family B�+mn n(V ) defined by (3). Bmn n(V ) is ... more In this article, we introduce the distributional family B�+mn n(V ) defined by (3). Bmn n(V ) is a generalization of distributional family R�(u) defined by (6), due to Y. Nozaki and this is called in (2) the Marcel Riesz Ultrahyperbolic Kernel. We obtain the formula L k {B�+mn n(V )} = C�,m,nB�+mn n 2km(V ) and evaluate B�+mn n(V ) at � = −2m( n + k − n 2m ) for the cases: µ = 2ms + m,
En este articulo se introduce la familia de funciones distribucionales ( ) 2 B x definida en ... more En este articulo se introduce la familia de funciones distribucionales ( ) 2 B x definida en (1) y usando laTransformada de Fourier se obtienen propiedades para los casos 0, 2k y 2k,k 1,2,... Usando la Transformada de Fourier, ( ) 2 B x puede ser expresada como combinacion lineal de y sus derivadas (ver, formula (27) y le damos un sentido a la propiedad ( ) ( ) 2 2 B x B x (ver, formula (44)) donde el simbolo significa convolucion. En la formula (33) aparece una nueva expresion para la delta de Dirac (x). Por otra parte, se introduce la familia de funciones distribucionales ( ) 2 M x definida en (54) y para 2k,E (x) k (ver, formula (62)) es solucion elemental del operador 2 2 1 dx d iterado k -veces
Sea M=M(x_1,…x_n ) una forma cuadratica definida en (18), en este articulo se define la distribuc... more Sea M=M(x_1,…x_n ) una forma cuadratica definida en (18), en este articulo se define la distribucion (M±i0)^λy se encuentra el residuo en λ=-n/2m-k/m m=1,2,…y k=0,1,2,… como consecuencia se obtiene la propiedad F_(-2km)^±=L_a^k {δ(x)} (ver formula (42)), donde F_α^± es la familia de funciones distribucionales definida por (35) y L_a^k es el operador definido por (39) y δ(x) es la distribucion delta de Dirac. Finalmente usando la transformada de Fourier de F_α^± se le da un sentido al producto de convolucion L_a^k {δ(x)}*L_a^l {δ(x)} (ver formula (59). Los resultados obtenidos en este articulo son generalizaciones de formulas que aparecen en ([1], pagina 353, ([2])) y ([3]) pagina 346, formula 5.4. Clasificacion segun AMS: 46F10 Palabras Claves: Distribucion; Residuo; Transformada de Fourier.
RESUMEN Sea P Px 1 ,. .. . , x n una forma cuadrática en n variables definida por (1) y sea ... more RESUMEN Sea P Px 1 ,. .. . , x n una forma cuadrática en n variables definida por (1) y sea P la distribución definida por (3) donde es un número complejo. Usando el desarrollo en serie de Laurent de P y considerando las signaturas p, q de Px, damos un sentido a los productos distribucionales P l .
In this note we give a sense to certain kinds of n‐dimensional distributional Hankel transforms o... more In this note we give a sense to certain kinds of n‐dimensional distributional Hankel transforms of the Dirac measure δ(k)(m2 + P). The most important result is the interchange formula between the product and the convolution of the Hankel transform of δ(k)(m2 + P).
In this paper we generalize the result obtained by Gonzáles Domínguez, Scarfiello and Fisher (A. ... more In this paper we generalize the result obtained by Gonzáles Domínguez, Scarfiello and Fisher (A. Gonzáles Domínguez and R. Scarfiello, Rev. Un. Mat. Argentina, Volumen de Homenaje a Beppo Levi (1956) 58–67; B. Fisher, Proc. Cambridge Philos. Soc. 72 (1972) 201–204). This result can be used in quantum field theory for the evaluation of products of propagators of the fields.
Journal of Mathematical Chemistry - J MATH CHEM, 2000
In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\d... more In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta ^{(k - 1)} (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}$$ and $$\delta ^{(k - 1)} (x_0 - \left| x \right|) \cdot \delta ^{(k - 1)} (x_0 + \left| x \right|)$$ . The first of them is a generalization of the product $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}{\text{ }}$$ given in [1, p. 158].
The present note contains the Tables of Fourier, Laplace and Hankel transforms of several dimensi... more The present note contains the Tables of Fourier, Laplace and Hankel transforms of several dimensional generalized functions. They are, mainly, based on the Laplace transform of retarded, Lorentz-invariant functions and the Fourier transforms of causal distributions.
In our former paper, [1], we have obtained an expansion for ([1], [pp. 123-125]), considering the... more In our former paper, [1], we have obtained an expansion for ([1], [pp. 123-125]), considering the cases n odd and n even separately. In the case n even, the formula obtained is under the conditions . The case was not studied. The main purpose of this paper is to extend the formula (∗) for considering two posibilities: a) p and q even; b) p and q odd.
Let P(x) be a quadratic form defined by (1).We know from(Gelfand and Shilov 1964)) that the equat... more Let P(x) be a quadratic form defined by (1).We know from(Gelfand and Shilov 1964)) that the equation {u(1 , 2 ,. .)} =f(x1,...xn) is often called ultrahyperbolic, where P=P(x) is defined by(31)and by (5). In this article we give a sense the elementary solution of the equation {u(1 , 2 ,. .)} =f(x1,...xn) where is the operator L{P} iterated m-times. {u(1 , 2 ,. .)} =f(x1,...xn
In this note we establish the distributional eonvolution produets of the form (P ± iD)> '... more In this note we establish the distributional eonvolution produets of the form (P ± iD)> ' * c5(Io} (p+) (e.E. (1,2,12), (1,1,40), (1, 1,41), (1, 1,42) and (1,1,43)) and (m2 + P ± iD)> ' * c5(Io} (m2 + P) (e.E. (1,3,4), (1,3,5), (1,3,6), (1,3, 7) and (1,3,8)). We obtain the results by using systematieally the Fourier transformation and to obtain (m2 + P ± iD)a-l * c5(Io} (m2 + P) we have employ the expansion c5(Io} (m2 + P) = L: (:2r c5(Io+JI}(P+) JI?:,:o (e.E. [2] , page 6, formula (1, 1,24)). The eonvolution produet (P ± iD)> ' * c5(Io} (p+) generalizes the result ([1] , page 13, formula (1,3,6)).
En este artículo se le dio un sentido al producto de convolución de δ (k-1)(1- x2)∗δ (l-1) (1- x2... more En este artículo se le dio un sentido al producto de convolución de δ (k-1)(1- x2)∗δ (l-1) (1- x2). Como caso particular se obtuvo una fórmula del producto de convolución de δ (1- x2)∗δ (1- x2) (C.f. fórmula (38)). Palabras Claves: Convolución; ProductoDOI: http://dx.doi.org/10.5377/nexo.v22i2.45Nexo Revista Científica Vol. 22, No. 02, pp.66-71/Diciembre 2009
Uploads
Papers by Manuel Aguirre