Operator theory on Hilbert spaces

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 237 in Sci. Bldg. A

• Description : the pdf file

• Schedule : Wednesday 8.45 - 10.15 in room 309 of the Math Building
  

• Class dates :
  April 17, 24
  May 8, 15, 22, 29
  June 5, 12, 19, 26
  July 2, 3, 10, 17
  

• Lecture notes : Full document: (100 pages)

• Lecture notes :
  Title: Operator theory on Hilbert spaces
  Contents
  Chapitre 1: Hilbert spaces and bounded linear operators
  Chapitre 2: Unbounded operators
  Chapitre 3: Examples
  Chapitre 4: Spectral theory for self-adjoint operators
  About stability of essential spectrum: presentation of Yukino Takeuchi with zoom or fixed camera
  Chapitre 5: Scattering theory
  Chapitre 6: Commutator methods
  Bibliography

• Student reports :
  Several exercises of Chapter I, by Kazumasa Narita
  Additional exercises on Chapter I and II, by Kazumasa Narita
  Integral operator and trace theorem, by Masakazu Tsuda
  Some exercises, and an extension on differential operators with smooth coefficients, by Xin Chen
  Some exercises on differential operators and Weyl calculus, by Ziyu Liu
  Exercise 1.3.2, by Daiki Uda
  Exercises 2.3.2 and 3.1.5, by Daichi Fujiwara
  Friedrichs extension, by Masakazu Tsuda
  Some exercises in Chapter 2, by Xin Chen
  On spectral measure, by Kazumasa Narita
  On spectral mapping theorem, by Daichi Fujiwara
  On spectral measure and spectrum of self-adjoint operators, by Ziyu Liu
  On spectral measure and spectrum of self-adjoint operators, by Kazuki Hattori
  Spectral decomposition and Weyl sequences, by Zhou Yuanting
  About Stieltjes measures, by Xin Chen
  A few exercises of chapters 1, 2 and 4, by Takafumi Tsukazaki
  Exercises of chapters 1 and 3, by Chen Jiawei
  On measures and the spectral measure, by Chen Jiawei (not available yet)
  A few exercises of chapters 1 to 4, by Daiki Uda
  

• References : (electronic version available upon request)
  [Amr] W. Amrein, Hilbert space methods in quantum mechanics, Fundamental Sciences. EPFL Press, Lausanne 2009.
  [ABG] W. Amrein, A. Boutet de Monvel, V. Georgescu, Co-groups, commutator methods and spectral theory of N-body Hamiltonians, Birkhauser, Basel, 1996.
  [BM] H. Baumgartel, M. Wollenberg, Mathematical scattering theory, Birkhauser verlag, Basel, 1983.
  [BDG] L. Bruneau, J. Derezinski, V. Georgescu, Homogeneous Schroedinger operators on half-line, Ann. Henri Poincare 12 no. 3 (2011), 547 - 590.
  [DR] J. Derezinski, S. Richard, On Schroedinger operators with inverse square potentials on the half-line, Ann. Henri Poincare 18 (2017), 869 - 928.
  [Kat] T. Kato, Perturbation theory for linear operators, Classics in mathematics, Springer, 1995.
  [Mur] G.J. Murphy, C*-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990.
  [Ped] G. Pedersen, Analysis now, Graduate texts in mathematics 118, Springer, 1989.
  [RS3] M. Reed, B. Simon, Methods of modern mathematical physics III: scattering theory, Academic Press, Inc., 1979.
  [RS4] M. Reed, B. Simon, Methods of modern mathematical physics IV: analysis of operators, Academic Press, Inc., 1978.
  [Ric] S. Richard, Levinson's theorem: an index theorem in scattering theory, in Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014, Operator Theory Advances and Applications 254, 149 - 203, Birkhauser, 2016.
  [Tes] G. Teschl, Mathematical methods in quantum mechanics, with applications to Schroedinger operators, Graduate Studies in Mathematics 99, American Mathematical Society, Providence, RI, 2009.
  [Yaf] D.R. Yafaev, Mathematical scattering theory. General theory, Translations of Mathematical Monographs 105, American Mathematical Society, Providence, RI, 1992.