Operator theory on Hilbert spaces
Contact:
Serge Richard (richard@math.nagoyau.ac.jp), Rm. 237 in Sci. Bldg. A

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

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 selfadjoint operators, by Ziyu Liu
On spectral measure and spectrum of selfadjoint 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,
Cogroups, commutator methods and spectral theory of Nbody
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 halfline,
Ann. Henri Poincare 12 no. 3 (2011), 547  590.
[DR] J. Derezinski, S. Richard,
On Schroedinger operators with inverse
square potentials on the halfline, 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.
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