Research and Innovation Articles
Pseudo-differential operators definedon Borel measures
Published 2013-07-29
Keywords
- Pseudo-differential operators,
- Borel measures,
- Radon-Nikodým Theorem,
- Boundedness and compactness of operators,
- Distributions, Ellipticoperators
How to Cite
Cardona, D. (2013). Pseudo-differential operators definedon Borel measures. Revista Integración, Temas De matemáticas, 31(1), 25–42. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3381
Abstract
In this paper we introduce a type of pseudo-differential operators defined on Borel measures. Classically the definition of pseudo-differential operators extends the tempered distributions space, but in its representation does not intervene the Fourier analysis in measures spaces. The main objective is to define such operators at a different angle and establish boundedness results on suitable normed spaces, in addition to providing a connection withthe pseudo-differential operators theory with symbols in the classes Sm, defined on Rn and the torus Tn.
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References
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[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.