Lecture notes

2018 Functional Analysis and Complex Analysis: graduate course

Nicola Arcozzi and Pavel Mozolyako

Schedule and syllabus:

https://phd.unibo.it/matematica/it/didattica/2018-2019

The course is self-contained and self-motivated, but it is also meant to introduce basic concepts that will be used in the course of prof. Baranov on De Branges spaces.

Some references:

Jim Agler, John E. McCarthy, Pick interpolation and Hilbert function spaces. Graduate Studies in Mathematics, 44. American Mathematical Society, Providence, RI, 2002. xx+308 pp. 

P. Duren, Theory of Hp spaces. Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London 1970 xii+258 pp. 

J. Garnett, Bounded analytic functions. Revised first edition. Graduate texts in Mathematics, 236. Springer, New York, 2007. xiv+459 pp. ISBN: 978-0-387-33621-3; 0-387-33621-4

B. Ya. Levin Lectures on entire functions. In collaboration with and with a preface by Yu. Lyubarskii, M. Sodin and V. Tkachenko. Translated from the Russian manuscript by Tkachenko. Translations of Mathematical Monographs, 150. American Mathematical Society, Providence, RI, 1996. xvi+248 pp. 

M. Reed, B. Simon, Methods of modern mathematical physics. I. Functional analysis. Academic Press, New York-London, 1972. xvii+325 pp. 

More readings (good for a seminar):

H. S. Shapiro, A. L. Schields  On the zeros of functions with finite Dirichlet integral and some related functions spaces.

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46291/209_2005_Article_BF01162379.pdf?sequence=1&isAllowed=y

Arthur Gretton Reproducing kernel Hilbert spaces in Machine Learning

http://www.gatsby.ucl.ac.uk/~gretton/coursefiles/Slides4A.pdf

John McCarthy Pick's Theorem - What's the Big Deal?

https://www.math.wustl.edu/~mccarthy/public_papers/wtbd_monthly.pdf

CALISTA BERNARD: INTERPOLATION THEOREMS AND APPLICATIONS (Riesz-Thorin)

http://math.uchicago.edu/~may/REU2013/REUPapers/Bernard.pdf

Jonathan Partington Infinite-dimensional systems (applications to Control Theory)

http://www1.maths.leeds.ac.uk/~pmt6jrp/dalfsen3.pdf

http://www1.maths.leeds.ac.uk/~pmt6jrp/feedback.pdf

Gilad Lerman The Shannon Sampling Theorem and Its Implications

http://www-users.math.umn.edu/~lerman/math5467/shannon_aliasing.pdf

Christopher Genovese Notes on Generating Functions

http://www.stat.cmu.edu/~genovese/class/iprob-S06/notes/generating-functions.pdf

Gerald B. Folland and Alladi Sitaram  The Uncertainty Principle: A Mathematical Survey 

https://link.springer.com/content/pdf/10.1007%2FBF02649110.pdf

Hidetosi Takahasi Complex Function Theory and Numerical Analysis

https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=41&iss=4&rank=10

Dana P. Williams LECTURE NOTES ON THE SPECTRAL THEOREM 

https://www.math.dartmouth.edu/~dana/bookspapers/ln-spec-thm.pdf

Alexandros Soumelidis (Chapt. 2, sections on the Takenaka-Malmquist system)

https://repozitorium.omikk.bme.hu/bitstream/handle/10890/141/ertekezes.PDF;sequence=1

Hannu Toivonen Robust Control Methods

http://users.abo.fi/htoivone/courses/robust/


Anton Baranov

INdAM graduate lectures: The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators

Anton Baranov

22/01 - 06/02 2019

Notes of Roman Romanov on

Canonical systems and de Branges spaces

https://arxiv.org/abs/1408.6022

The lecture notes of the course are on the right column of the page.

Videos of the course

22/01

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23/01

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29/01

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30/01

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05/02

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06/02

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