Dear colleagues,
We are pleased to invite you to the second lecture in the five-part series organized by QOART (Quantum Optics and Related Topics), devoted to infinite-dimensional functional analysis and the isospectrality problem for the Schrödinger equation.
QOART Online Seminar — Friday, 13 November 2026
Speaker: S. A. Titarenko
Lecture Series: Infinite-Dimensional Analysis in the Isospectrality Problem for the Schrödinger Equation
Lecture 2: Operators as Functions of Functions and Their Spectral Classification
Date and Time: Friday, 13 November 2026, at 16:00 Moscow time (UTC+3)
Duration: Approximately 90 minutes, including a short break and discussion.
Language: English
Link to Join: For security reasons, the meeting link is temporarily available upon request. To receive the connection details, please contact the seminar organizer at ranjit.singh@mail.ru
Abstract:
This lecture examines the spectral classification of operators in finite- and infinite-dimensional spaces, focusing on self-adjoint and positive-definite operators. Particular attention is given to the connections between functional analysis and quantum mechanics, including isospectral Hamiltonians, quantum billiards, and examples of non-unique isospectral Hamiltonians.
The lecture also addresses the Schrödinger equation in Sobolev spaces, double unitary operators, and the transition from abstract function spaces to geometry. Further topics include induced topology, distributive lattices, and the finiteness of the number of connected components in disconnected domains.
Lecture Outline:
Self-adjoint and positive-definite operators.
Comparison of finite- and infinite-dimensional spectral classification.
Physical interpretation of spectral classification: isospectral Hamiltonians and quantum billiards.
Non-uniqueness of isospectral Hamiltonians: examples from 1992–2010.
The Schrödinger equation in Sobolev spaces:
Double unitary operators and isospectrality in infinite-dimensional analysis.
From abstract function spaces to geometry, following Lebesgue's ideas.
Induced topology and distributive lattices: toward a new logic.
Finiteness of the number of connected components in disconnected domains.
QOART Seminar Website: https://sites.google.com/view/qoart/seminar
We would appreciate it if you could share this announcement with interested colleagues and students.
We look forward to welcoming you to the seminar!
Best regards,
Ranjit
+7 909 680 67 87
https://www.mathnet.ru/eng/person86793
QOART Telegram Channel: https://t.me/+i6rnhM_Wp1YwY2Ji
Optical ‘Cat-like’ State: https://www.mathnet.ru/eng/present47506
QOART 2026 Conference: https://sites.google.com/view/qoart/2026
QOART Seminar: https://sites.google.com/view/qoart/seminar
