Artículos científicos
Publicado 2013-07-29
Palabras clave
- Operadores pseudodiferenciales,
- Medidas de Borel,
- Teorema de Radon-Nikodým,
- Continuidad y compacidad de operadores,
- Distribuciones
- Operadores elípticos ...Más
Cómo citar
Cardona, D. (2013). Operadores pseudodiferenciales definidos en medidas de Borel. Revista Integración, Temas De matemáticas, 31(1), 25–42. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3381
Resumen
En este trabajo se introduce un tipo de operadores pseudodiferenciales definidos en medidas de Borel. Clásicamente la definición de operadores pseudodiferenciales se extiende al espacio de las distribuciones temperadas; sin embargo, en su representación no interviene el análisis de Fourier en espacios de medidas. El objetivo principal es definir tales operadores en un ángulo diferente y establecer resultados de continuidad entre espacios normados adecuados, además de proporcionar una conexión con la teoría de operadores pseudodiferenciales con símbolos en las clases Sm, definidas en Rn y el toroTn.
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Referencias
[1] Ashiro R., Nagase M. and Vaillancourt R., “Pseudo-differential operators in Lp(Rn) spaces”,Cubo 6 (2004), no. 3, 91–129.
[2] Conway J., A Course in Functional Analysis, Springer-Verlag, New York, 1997.
[3] Calderón A. and Vaillancourt R., “On the boundedness of pseudo-differential operators”, J. Math. Soc. Japan 23 (1971), 374–378.
[4] Dieudonné J., “Recent development in the theory of linear partial differential equations”, Internat. J. Math. Math. Sci. 3 (1980), no. 1, 1–14.
[5] Duoandikoetxea J., Fourier Analysis, 29. American Mathematical Society, Providence, 2000.
[6] Guzmán M., “Representación de medidas vectoriales”, Rev. Soc. Colombiana de Mat. 44 (2010), no. 2, 129–147.
[7] Hörmander L., The Analysis of Linear Partial Differential Operators III, Springer-Verlag, Berlín, 1985.
[8] Hwang I., “The L2-boundedness of pseudo-differential operators”, Trans. Amer. Math. Soc. 302 (1987), no. 1, 55–76.
[9] Kohn J. and Nirenberg L., “An Algebra of pseudo-differential operators”, Comm. Pure Appl. Math. 18 (1965), 269–305.
[10] Molahajloo S., “Pseudo-differential Operators on Z”, Oper. Theory Adv. Appl. 205 (2010), no. 1, 213–221.
[11] Restrepo G., Teoría de la Integración, Universidad del Valle, Colombia, 2004.
[12] Rodriguez C., “P-Estimates for Operators on Zn”, J. Pseudo-Differ. Oper. Appl. 1 (2010), no. 2, 367–375.
[13] Ruzhansky M. and Turunen V., Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics, Pseudo-Differential Operators. Theory and Applications 2, Birkhäüser-Verlag, Basel, 2010.
[14] Schwartz L., Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, London, 1973.
[15] Stein E., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, New Jersey, 1993.
[16] Stein E., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey, 1971.
[17] Taylor M., Partial differential equations III. Non linear equations, Springer-Verlag, New York, 2011.
[18] Wong M.W., An Introduction to pseudo-differential operators. World Scientific Publishing, New Jersey, 1991.
[2] Conway J., A Course in Functional Analysis, Springer-Verlag, New York, 1997.
[3] Calderón A. and Vaillancourt R., “On the boundedness of pseudo-differential operators”, J. Math. Soc. Japan 23 (1971), 374–378.
[4] Dieudonné J., “Recent development in the theory of linear partial differential equations”, Internat. J. Math. Math. Sci. 3 (1980), no. 1, 1–14.
[5] Duoandikoetxea J., Fourier Analysis, 29. American Mathematical Society, Providence, 2000.
[6] Guzmán M., “Representación de medidas vectoriales”, Rev. Soc. Colombiana de Mat. 44 (2010), no. 2, 129–147.
[7] Hörmander L., The Analysis of Linear Partial Differential Operators III, Springer-Verlag, Berlín, 1985.
[8] Hwang I., “The L2-boundedness of pseudo-differential operators”, Trans. Amer. Math. Soc. 302 (1987), no. 1, 55–76.
[9] Kohn J. and Nirenberg L., “An Algebra of pseudo-differential operators”, Comm. Pure Appl. Math. 18 (1965), 269–305.
[10] Molahajloo S., “Pseudo-differential Operators on Z”, Oper. Theory Adv. Appl. 205 (2010), no. 1, 213–221.
[11] Restrepo G., Teoría de la Integración, Universidad del Valle, Colombia, 2004.
[12] Rodriguez C., “P-Estimates for Operators on Zn”, J. Pseudo-Differ. Oper. Appl. 1 (2010), no. 2, 367–375.
[13] Ruzhansky M. and Turunen V., Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics, Pseudo-Differential Operators. Theory and Applications 2, Birkhäüser-Verlag, Basel, 2010.
[14] Schwartz L., Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, London, 1973.
[15] Stein E., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, New Jersey, 1993.
[16] Stein E., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey, 1971.
[17] Taylor M., Partial differential equations III. Non linear equations, Springer-Verlag, New York, 2011.
[18] Wong M.W., An Introduction to pseudo-differential operators. World Scientific Publishing, New Jersey, 1991.