Special Mathematics Lecture

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

Introduction to functional analysis (Fall 2019)

Registration code : 0063611
Schedule : Wednesday (18:30 - 20.00) in room 207 of the Science Building A

• Syllabus : the pdf file

• Class dates :
  October 2, 9, 23, 30
  November 6, 13, 20, 27
  December 4, 11, 18
  January 8, 15, 22
  

• Study sessions: Every Tuesday, 6.30 - 8.00, in room 207 of Science Building A.

• Program :
  Distribution theory: lect. 1, lect. 2, lect. 3
  Lebesgue theory: lect. 4, lect. 5, lect. 6
  Operator theory on Hilbert spaces: lect. 7, lect. 8, lect. 9, lect. 10, lect. 11, lect. 12
  Spectral theory for self-adjoint operators lect. 12, lect. 13, lect. 14

• The cumulative notes : Introduction to functional analysis (42 pages, handwritten notes taken by Liyang Zhang)

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, please contact me or Xin Chen

• Works submitted by the students :
  On distribution defined by 1/|x| by Tomoya Tatsuno
  On principal value of 1/x by Bui Tu Ha
  About some distributions by Liyang Zhang
  Some distributions and operations on distributions by Sun Chang
  On Lebesgue measurable sets by Liyang Zhang
  On Lebesgue measurable functions by Tomoya Tatsuno
  On a Lebesgue (but not Riemann) integrable function by Bui Tu Ha
  On volume of boxes by Bui Tu Ha
  Properties of Hilbert spaces by Sun Chang
  On strong and weak convergences by Bui Tu Ha and Shimura Koki
  Standard nequalities in Hilbert spaces, by Bui Tu Ha and Shimura Koki
  Inequalities in Hilbert spaces, weak and strong topology by Yi Liu
  On Weyl calculus by Liyang Zhang
  On standard commutation relations by Arata Suzuki and Bui Tu Ha
  Adjoint, and perturbation theory by Arata Suzuki and Bui Tu Ha
  Polarization identity by Arata Suzuki
  Adjoint, and standard commutation relations by Song Ha
  

• References : (electronic version available upon request)
  [Amr] W. Amrein, Hilbert space methods in quantum mechanics
  [GvD] G. van Dijk, Distribution theory: convolution, Fourier transform, and Laplace transform
  [Nel] F.S. Nelson, A user-friendly introduction to Lebesgue measure and integration