VIEJOS Y NUEVOS RESULTADOS SOBRE INTEGRALES SINGULARES E HIPERSINGULARES
PDF

Cómo citar

Horváth, J. . (2023). VIEJOS Y NUEVOS RESULTADOS SOBRE INTEGRALES SINGULARES E HIPERSINGULARES. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 29(113), 547–569. https://doi.org/10.18257/raccefyn.29(113).2005.2185

Descargas

Los datos de descargas todavía no están disponibles.

Métricas Alternativas


Dimensions

Resumen

Exposición de algunos trabajos del autor sobre integrales singulares e hipersingulares, publicados entre 1953 y 1987, completada con resultados nuevos, observaciones sobre contribuciones de otros matemáticos, simplificaciones y algunas correcciones.

https://doi.org/10.18257/raccefyn.29(113).2005.2185

Palabras clave

Operadores integrales singulares | transformada de Hilbert | distribuciones | convolución de distribuciones
PDF

Citas

Alvarez, Josefina; Carton-Lebrun, Christiane: Optimal spaces for the S'-convolutions with Marcel Riesz ker­nels and the N-dimensional Hilbert kernel. Analysis of di­vergence (Orono, ME, 1997), Appl. Numer. Harmon. Anal., Birkhiiuser, págs. 233-248.

Bjéirck, Jan-Erik: Rings of differential operators. North­Holland, Amsterdam, 1979.

Bochner, Saloman: Vor/esungen über Fouriersche Jnte­grale. Akademische Verlagsgesellschaft, Leipzig, 1932.

Bochner, Saloman: Theta relations with spherical harmonics. Proc. Nat. Acad. Sci. USA 37 (1951), 804-808.

Calderón, Alberto P.: On theorems of M. Riesz and Zyg­mund. Proc. Amer. Math. Soc. 1 (1950), 533-535.

Calderón, Alberto P: On a problem of Mihlin. 'Irans. Amer. Math. Soc. '78 (1955), 209-224.

Calderón, Alberto P: On singular integrals. Amer. J. Math 78 (1956), 289-309.

Calderón, Alberto P: Singular integral operators and differential equations. Amer. J. Math. 79 (1957), 901-921.

Cartwright, Mary Lucy: Manttscripts of Hardy, Little­wood, Marce/ Riesz and Titchmarsh. !3ull. London Math. Soc. 14 (1982), 472-532.

Christ, Michael: Lectures on singular integral operators. Conf. Board of the Math. Sciences, Regional Conferences in Math., No. 77. Amer. Math. Soc., 1990.

Diaz, Joaquin B.: On a class of partial differential equa­tions of even arder. Amer. J. Math. 68 (1946), 611-659. Dierolf, Peter; Voigt, Jürgen: Convolution and S'-convolution of distributions. Collect. Math. 29 (1978), 185- 196.

Eskin, G. l.: Boundary value problems for el/iptic pseudo­r differential equations. Tanslations of Mathematical Mono­graphs, Vol. 52. Amer Math. Soc., 1981.

Fefferman, C.; Stein, E. M.: HP spaces of several varia­bles. Acta Math. 129 (1972), 137-193.

Fefferman, Charles: Selected theorems by Eli Stein. Es­says on Fourier analysis in honor of Elias M. Stein, ed.: Ch. Fefferman, R. Fcfferman, St. Wainger. Princeton University Press, 1995, págs. 1-35.

Fueter, R.: Die Funktionentheorie der Differentialglei­chungen 6u = O und 66u = O mit v-ier reellen Variablen. Commentarii Math. Helvetici 7 (1934/35), 307-330.

Giraud, Georges: Sur une classe générale d'équations a intégrales principales. C.R. Acad. Sci. París 202 (1936), 2124-2127.

Giraud, Georges: Complément a un résultat sur les équations ó. intégrales principales. C.R. Acad. Sci. Paris 203, 292-294. Hardy, G. H.; Littlewood, J. E.; Pólya, G.: Jnequali­ties. Cambridge University Press, 1934.

Hirata, Yukio: On convolutions in the theory of distribu­tions. J. of Science of the Hiroshima University, Ser. A, 22 (1958), 89-98.

Hirata, Y.; Ogata, Hayao: On the exchange formula for distribul'ions. Journal of Science of the Hiroshima Universi­ty, Ser. A. 22 (1958), 147-152.

Héirmander, Lars: Pseudo-differential operators. Comm. Pure Applied Math. 18 (1965), 501-517.

Héirmander, Lars: Pseudo-clifferenlial operat.ors ancl non-elliptic bound­ari; problems. Ann. of Math. 83 (1966), 129-209.

Héirmander, Lars: Pseudo-diffcrential operators and hypoelliptic equa­tions. Singular Integrals, Procecdings of Symposia in Pure lVIathematics, Vol. 10. Amer. Math. Soc., 1967, págs. 138- 183.

Héirmander, Lars: The analysis of linear partial differential operators f. Grundlehren der mathematischen Wissenschaften 256. Springer, 1983.

Héirmander, Lars: The analysis of linear partial difjerential operators III. Grundlehren der mathematischen Wissenschaften 274. Springer, 1985.

Horváth, J.: Sur les fonctions conjuguées d plusieurs va­riables. Indag. Math. 15 (1953), 17-29.

Horváth, J: Singular integral operators and spherical harmonics. Trans. Amer. Math. Soc. 82 (1956), 52-63.

Horváth, J: Basic sets of polynomial solutions for partial differential equations. Proc. Amer. Math. Soc. 9 (1958), 569-575.

Horváth, J: On some composition formulas. Proc. Amer. Math. Soc. 10 (1959), 433-437.

Horváth, J: A generalization of the Cauchy-Riemann equations. Contributions to Diff. Equations 1 (1961), 39-58.

Horváth, J: Finite parts of distributions. Linear operators and approximations (Oberwolfach, August 14-22, 1971). Internat. Series Num. Math., Vol. 20. Birkhäuser, 1972, págs. 142-158.

Horváth, J: Distribuciones definidas por prolongación analítica. Rev. Colombiana Mat. 8 (1974), 47-95.

Horváth, J: Sur la convolution des distributions. Bull. Sci. Math.98 (1974), 183-192.

Horváth, J: Composition of hypersingular integral operators. Applicable Analysis 7 (1978), 171-190.

Horváth, J: Convolution des noyaux hypersinguliers. G. Choquet, M. Rogalski, J. Saint-Raimond (Eds.), Séminaire initiation á l'analyse, 19e année, 1979/80, expose no. 8. Univ París VI, 1980, págs. 1-17.

Horváth, J.; Ortner, N.; Wagner·, P.: Analytic continuation and convolution of hypersingular higher Hilbert-Riesz kernels. J. Math. Anal. Appl. 123 (1987), 429-447.

Humbert, Pierre: Potentiels et prépotentiels. Cahiers Scientifiques, fasc. 15. Gauthier-Villars, Paris, 1936.

Katznelson, Yitzhak: An introduction to harmonic analysis. Dover, New York, 1976.

Ketchum, P. W.: A complete solution of Laplace's equation by an infinite hypervariable. Amer. J. Math. 51 (1929), 179-188.

Kohn, J. J.: Singular integral equations for differential forms on Riemannian manifolds. Proc. Nat. Acad. Sci. USA 42 (1956), 650-653.

Kohn, J. J.; Nirenberg, L.: An algebra of pseudodifferential operators. Comm. Pure Applied Math. 18 (1965), 269-305.

Kumano-go, Hitoshi: Pseudo-differential operators. MIT Press, Cambridge, MA, 1974.

Lammel, Ernst: Generalizaciones de la teoría de las funciones de variables complejas. Segundo symposium sobre algunos problemas matemáticos que se están estudiando en Latinoamérica, Villavicencio-Mendoza, 1954. UNESCO, págs. 191-197.

Leray, Jean: Hyperbolic differential equations. The Institute of Advanced Study, Princeton, N.J., 1953, 1955.

Littlewood, J. E.: A mathematicians miscellany. Methuen, London, 1953, 1957.

Magnus, W; Oberhettinger, F.: Formulas and theorems for the special functions of mathematical physics. Chelsea, New York, 1949.

Mihlin, S. G.: Singular integral equations. Amer. Math. Soc. Translations, Ser 1, Vol. 10, 1962, págs. 84-198.

Miles, E. P. jr.: Three dimensional harmonic functions generated by analytic functions of a hypervariable. Amer. Math. Monthly 61 (1954), 694-697.

Lammel, Ernst: The analytic Cauchy problem for the iterated wave equation. Portugaliae Math. 18 (1959), 111-119.

Miles, E. P.; Williams, Ernest: A basic set of of homogeneous harmonic polynomials in k variables. Proc. Amer. Math. Soc. 6 (1955), 191-194.

Miles, E. P.; Williams, Ernest: A note on basic sets of homogeneous harmonic polynomials. Proc. Amer. Math. Soc. 6 (1955), 769-770.

Miles, E. P.; Williams, Ernest: The Cauchy problem for linear partial differential equations with restricted boundary conditions. Canadian J. Math. 8 (1956), 426-431.

Miles, E. P.; Williams, Ernest: A basic set of polynomial solutions for the Euler-Poisson-Darboux and Beltrami equations. Amer. Math. Monthly 63 (1956), 401-404.

Miles, E. P.; Williams, Ernest: Basic sets of polynomials for the iterated Laplace and wave equations. Duke Math. J. 26 (1959), 35-40.

Miles, E. P.; Young, E. C.: Basic sets of polynomials for generalized Beltrami and Euler-Poisson-Darboux equations and their iterates. Proc. Amer. Math. Soc. 18 (1967), 981-986.

Okikiolu, George O.: Special integral operators, Vol. II - Poisson operators, conjugate operators and related integrals. Okikiolu Sci. and Industr. Org., London, 1981.

Ortiz F., Alejandro: Operadores integrales singulares. Universidad Nacional de Trujillo, Depto. de Matemática, Trujillo, Perú, 1972.

Ortner, Norbert: Faltung hypersingulärer integraloperatoren. Math. Ann. 248 (1980), 19-46.

Ortner, Norbert: Sur la convolution des distributions. C.R. Acad. Sci. París, Sér A-B 290 (1980), 533-536.

Ortner, Norbert: Convolution des distributions et des noyaux euclidiens. G. Choquet, M. Rogalski, J. Saint - Raimond (Eds.), Séminaire initiation a l'analyse, 19e année, 1979/1980, exposé no. 12. Univ Paris VI, 1980, págs. 1-11.

Ortner, Norbert: Analytic continuation and convolution of hypersingular higher Hilbert-Riesz kernels. Alfred Haar memorial conference, Budapest, 1985, págs. 675-685.

Ortner, Norbert: On some contributions of John Horváth to the theory of distributions. J. Math. Anal. Appl. 297 (2004), 353-383.

Ortner, N.: Wagner, P.:Convolution groupsfor cuasihyperbolic systems of differential operators.

Plessner, A.: Zur Theorie der konjugierten trigonometrischen Reihen. Mitteilungen Math. Seminar Gieben 10 (1923), 1-36.

Protter, M. H.: Generalized spherical harmonics. Trans. Amer. Math. Soc. 63 (1948), 314-341.

Protter, M. H.: On a class of harmonic polynomials. Portugaliae Math. 10 (1951), 11-22.

Riesz, Frigyes: Über die Randwerte einer analytischen Funktion. Math. Zeitschrift 18 (1923), 117-124; (Euvres complétes, Budapest, 1960, D7, págs. 645-653.

Riesz, Marcel: Sur la sommation des séries de Fourier. Acta Sci. Math. Szeged 1 (1923), 104-113.

Riesz, Marce: Sur les fonctions conjuguées Math. Zeitschrift 27 (1927), 218-244.

Riesz, Marce: L'intégrale de Riemann-Liouville et le probléme de Cauchy. Acta Math. 81 (1949), 1-223.

Riesz, Marce: Collected papers. Springer-Verlag, 1988.

Roider, Bernhard: Surla convolution des distributions. Bull. Sci. Math. 100 (1976), 193-199.

Rudin, Walter: Fourier· analysis on grous. Wiley, 1962, 1990.

Rudin, Walter: Hypersingular integrals and their applications. Taylor and Francis, London, 2002.

Schaad, Margrit: Über eine Klasse van rechtsregulären Funktionen mit 2n reellen Variablen. Disertación, Zurich, 1944.

Schwartz, Laurent: Théorie des distributions. Nouvelle édition. Hermann, Paris, 1966.

Schwartz, Laurent: Produits tensoriels topologiques d'espaces vectoriels topologiques. Espaces vectoriels topologiques nucléaires. Applications. Séminaire, Institut Henri Poincaré, Paris, 1954.

Schwartz, Laurent: Distributions a valeurs vectorielles I. Ann. Institut Fourier Grenoble 7 (1957), 1-141.

Schwartz, Laurent: Distributions á valeurs vectorielles II. Ann. Institut Fourier Grenoble 8 (1959), 1-209.

Seeley, R. T.: Elliptic singular integral equations. Singular Integrals, Proceedings of Symposia in Pure Mathematics, Vol. 10, Amer. Math. Soc. 1967, págs. 308-315.

Shiraishi, Risai: On the definition of convolutions for distributions. J. Sci. Hiroshima University, Ser. A 23 (1959), 19-32.

Simanca, S. R.: Pseudo-differential operators. Pitman Research Notes in Math. Series 236. Longman Scientific and Technical, Harlow, Essex, UK, 1990.

Staub, Alfred: Integralsätze hyperkomplexer, regulärer Funktionen van 2n reellen Variablen. Disertación, Zurich, 1946.

Stein, Elias M.: Singular integrals and differentiability properties of functions. Princeton University Press, 1971.

Harmonic analysis: real-variable methods, orthogonality and oscillatory; integrals. Princeton University Press, 1993.

Stein, E. M; Weiss, G.: On the theory of harmonic functions of several variables I, The theory of HP spaces. Acta Math. 103 (1960), 25-62.

Stein, E. M; Weiss, G.: On the theory of harmonic functions of several variables II, Behavior near the boundary. Acta Math. 106 (1961), 137-174.

Stein, E. M; Weiss, G.: Introduction to Fourier analysis in Euclidean Spaces. Princeton University Press, 1971.

Taylor, Michael E.: Pseudodifferential operators. Princeton University Press, 1981.

Thorin, G. 0.: An extension of a convexity theorem due to M. Riesz. Kungl. Fysiografiska Sälskapets i Lund Förhandlinger 8 (1938), no. 14.

Thorin, G. 0.-: Convexity theorems generalizing those of M. Riesz and Hadamard, with some applications. Disertación Lund, Meddelanden fran Lunds Universitets Matematiska Seminarium, Vol. 9 (1948).

Titchmarsh, E. C.: Introduction to the theory of Fourier· integrals. Cambridge University Press, 1948.

Treves, Francois: Introduction to pseudodifferential and Fourier integral operators. Vol. 1, Pseudodifferential operators. Plenum, New York, 1980.

Unterberger, A; Bokobza, J.: Les operateurs de Calderón-Zygmund précisés. C.R. Acad. Sci. Paris 259 (1965), 1612-1614.

Wagner, Peter: Zur Faltung van Distributionen. Math. Ann. 276 (1987), 467-485.

Wagner, Peter-: Bernstein-Sato-Polynome und Faltungsgruppen zu Differentialoperatoren. Zeitschrift für Analysis und ihre Anwendungen 8 (1989), 407-423.

Weiss, Guido: Análisis armónico en varias variables. Teoría de los espacios HP. Cursos y seminarios matemáticos, fasc. 9, Universidad de Buenos Aires, 1960.

Wicht, M. C.: Recursion and interrelation for Miles­ Williams biharmonics. Amer. Math. Monthly 64 (1957), 463.

Yoshinaga, Kyoichi; Ogata, Hayao: On convolutions. J. of Science of the Hiroshima University, Ser A 22 (1968) 15-24

Zaidman, S.: Distributions and pseudo-differential operators. Pitman Research Notes in Math. Series 248, Longman Scientific and Technical, Harlow, Essex, UK, 1991.

Zaidman, S.: Topics in pseudo-differential operators. Pitman Research Notes in Math. Series 359, Longman, Harlow, Essex, UK, 1996.

Zygmund, Antoni: Trigonometric series, Second edition. Cambridge University Press, 1959.

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.

Derechos de autor 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales