純粋・応用数学・数学隣接分野（含むガロア理論）20

[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）20 (1002ﾚｽ)
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494: １３２人目の素数さん [] 2025/06/09(月) 12:50:47.47 ID:n21sjwUN

>>493
ID:ISVAs415 は、御大か
巡回ありがとうございます。

下記ですね
en.wikipedia に、pdfのリンクがあって、全文読めますね

(参考)
https://en.wikipedia.org/wiki/DBAR_problem
DBAR problem
The DBAR problem is of key importance in the theory of integrable systems, Schrödinger operators and generalizes the Riemann–Hilbert problem.[1][2][3]

References
[2]Haslinger, Friedrich (2014). The d-bar Neumann Problem and Schrödinger Operators. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-031535-6.
PDF
https://www.mat.univie.ac.at/~has/dbar/dbar1.pdf
Preface
The rst chapters contain a discussion
of Bergman spaces and of the solution operator to @ restricted to holomorphic
L2 -functions in one complex variable, pointing out that the Bergman kernel of the associated
Hilbert space of holomorphic functions plays an important role.

The next chapter contains a detailed account of the application of the @-methods to
Schr odinger operators, Pauli and Dirac operators and to Witten-Laplacians.

In this way one obtains a rather general basic
estimate, from which one gets H ormander's L2 -estimates for the solution of the CauchyRiemann
equation together with results on related weighted spaces of entire functions,
such as that these spaces are in nite-dimensional if the eigenvalues of the Levi-matrix
of the weight function show a certain behavior at in nity. In addition, it is pointed out
that some L2 -estimates for @ can be interpreted in the sense of a general Brascamp-Lieb
inequality.

Contents
Preface iii
1. Bergman spaces 2
2. The canonical solution operator to @ restricted to spaces of holomorphic
functions 10
3. Spectral properties of the canonical solution operator to @ 21
4. The @-complex 33
5. The weighted @-complex 50
6. The twisted @-complex 58
7. Applications 62
8. Schr odinger operators 69
9. Compactness 74
10. The @-Neumann operator and commutators of the Bergman projection and
multiplication operators. 85

https://www.mat.univie.ac.at/~has/
Friedrich Haslinger
Faculty of Mathematics
University of Vienna
Research interests
d-bar Neumann problem
Hardy and Bergman spaces in several complex variables
Bergman and Szegö kernels
Spectral analysis of Schrödinger operators

http://rio2016.5ch.net/test/read.cgi/math/1745503590/494

496: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/06/09(月) 15:14:42.61 ID:n21sjwUN

>>494
>Brascamp-Lieb inequality.

Liebさん
In 2022 the Carl Friedrich Gauss Prize at the International Congress of Mathematicians
In 2023 Lieb received Kyoto Prize in Basic Sciences for his achievements in many-body physics.[23]

https://en.wikipedia.org/wiki/Brascamp%E2%80%93Lieb_inequality
Brascamp–Lieb inequality

https://en.wikipedia.org/wiki/Elliott_H._Lieb
Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physicist. He is a professor of mathematics and physics at Princeton University. Lieb's works pertain to quantum and classical many-body problem,[1][2][3] atomic structure,[3] the stability of matter,[3] functional inequalities,[4] the theory of magnetism,[2] and the Hubbard model.[2]
Awards
In 2022
the Carl Friedrich Gauss Prize at the International Congress of Mathematicians ″for deep mathematical contributions of exceptional breadth which have shaped the fields of quantum mechanics, statistical mechanics, computational chemistry, and quantum information theory.″[16]
In 2023 Lieb received Kyoto Prize in Basic Sciences for his achievements in many-body physics.[23]

http://rio2016.5ch.net/test/read.cgi/math/1745503590/496

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