Avisos:
» Ya está disponible la Tarea
3. La fecha de entrega es el 5 de diciembre.
Sobre el curso:
Éste es un curso básico del área de Análisis. El objetivo
principal del curso es introducir al estudiante a las
herramientas básicas del Análisis Funcional, es decir, a la
teoría de espacios normados completos (espacios de Banach) y a
los operadores lineales definidos sobre tales espacios.
Contenido:
- Calendario 2025 (plan semestral): [PDF].
- Temario, calendario y bibliografía del curso [PDF].
- Página del Posgrado en Ciencias Matemáticas.
Material auxiliar:
- El lema de Zorn, el principio de maximalidad de Hausdorff y el axioma de elección [PDF].
- Les comparto las ligas a los siguientes artículos de S. Kesavan:
- S. Kesavan, A
note on the grand theorems of functional analysis,
Math. Newsl. 27 (2017), no. 3, pp. 188–191.
- S. Kesavan, The
grand theorems of functional analysis revisited: a
Baire-free approach. Math. Newsl. 31
(2020/21), no. 3, pp. 89–93.
Tareas:
- Tarea 1 [PDF].
Fecha de entrega: pasada..
- Tarea 2 [PDF].
Fecha de entrega: pasada.
- Tarea 3 [PDF].
Fecha de entrega: 5 de diciembre.
Bibliografía
Bibliografía básica:
- H. Brezis, Functional Analysis, Sobolev spaces, and Partial Differential Equations, Universitext Springer Verlag, 2011.
- S. Kesavan, Functional analysis, vol. 52 of Texts and Readings in Mathematics, Springer, Singapore; Hindustan Book Agency, New Delhi, second ed., 2023.
- E. Kreyszig, Introductory functional analysis with applications, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989.
- W. Rudin, Functional analysis, International
Series in Pure and Applied Mathematics, McGraw-Hill, Inc.,
New York, second ed., 1991.
Bibliografía complementaria:
- M. S. Birman and M. Z. Solomjak, Spectral theory of
selfadjoint operators in Hilbert space, Mathematics and
its Applications (Soviet Series), D. Reidel Publishing
Co., Dordrecht, 1987.
- A. Bressan, Lecture Notes on Functional Analysis, vol. 143 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2013.
- T. Bühler and D. A. Salamon, Functional analysis, vol. 191 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2018.
- J. B. Conway, A course in functional analysis, vol. 96 of Graduate Texts in Mathematics, Springer-Verlag, New York, second ed., 1990.
- N. Dunford and J. T. Schwartz, Linear operators. Volumes I-III. Wiley Classics Library, John Wiley & Sons Inc., New York, 1988.
- M. Haase, Functional analysis, vol. 156 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2014.
- P. D. Hislop and I. M. Sigal, Introduction to spectral theory, vol. 113 of Applied Mathematical Sciences, Springer-Verlag, New York, 1996.
- T. Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1980 edition.
- P. D. Lax, Functional analysis, Pure and Applied Mathematics (New York), Wiley- Interscience, John Wiley & Sons, New York, 2002.
- M. Reed and B. Simon, Methods of modern mathematical physics. Volumes I-IV. Academic Press – Harcourt Brace Jovanovich, Publishers, New York-London, 1975-1980.
- J. C. Robinson, An introduction to functional analysis, Cambridge University Press, London, 2020.
- M. Schechter, Principles of functional analysis, vol. 36 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second ed., 2002.
- K. Schmüdgen, Unbounded self-adjoint operators on
Hilbert space, vol. 265 of Graduate Texts in
Mathematics, Springer, Dordrecht, 2012.
- K. Yosida, Functional analysis, Classics in Mathematics, Springer-Verlag, Berlin, Sixth ed., 1980.