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

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