Remarks on a boundary value problem for a matrix valued $\overline{\partial}$ equation
DOI:
https://doi.org/10.33044/revuma.4326Abstract
In this short note, we discuss a boundary value problem for a matrix valued $\overline{\partial}$ equation.
Downloads
References
B. Berndtsson and J.-P. Rosay, Quasi-isometric vector bundles and bounded factorization of holomorphic matrices, Ann. Inst. Fourier (Grenoble) 53 no. 3 (2003), 885–901. MR Zbl Available at http://aif.cedram.org/item?id=AIF_2003__53_3_885_0.
M. S. Brodskiĭ, Triangular and Jordan representations of linear operators, Translations of Mathematical Monographs, Vol. 32, American Mathematical Society, Providence, RI, 1971. MR
B. Davey, C. Kenig, and J.-N. Wang, On Landis' conjecture in the plane when the potential has an exponentially decaying negative part, Algebra i Analiz 31 no. 2 (2019), 204–226, translation in St. Petersburg Math. J. 31 (2020), no. 2, 337–353. DOI MR Zbl
B. Davey, On Landis' conjecture in the plane for some equations with sign-changing potentials, Rev. Mat. Iberoam. 36 no. 5 (2020), 1571–1596. DOI MR Zbl
C. Kenig, L. Silvestre, and J.-N. Wang, On Landis' conjecture in the plane, Comm. Partial Differential Equations 40 no. 4 (2015), 766–789. DOI MR Zbl
V. A. Kondratʹev and E. M. Landis, Qualitative theory of second-order linear partial differential equations, in Partial Differential Equations, 3 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988, pp. 99–215, 220. MR Zbl
L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 no. 4 (1981), 427–474. MR Zbl Available at http://www.numdam.org/item?id=BSMF_1981__109__427_0.
A. Logunov, E. Malinnikova, N. Nadirashvili, and F. Nazarov, The Landis conjecture on exponential decay, 2020. arXiv 2007.07034 [math.AP].
V. P. Potapov, The multiplicative structure of $J$-contractive matrix functions, Amer. Math. Soc. Transl. (2) 15 (1960), 131–243. DOI MR
J. Roos, Inner-Outer Factorization of Analytic Matrix-Valued Functions, Master's thesis, Mathematisch-Naturwissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn, 2014. Available at https://faculty.uml.edu/joris_roos/files/MasterThesis.pdf.
A. Slavík, Product Integration, Its History and Applications, Nečas Center for Mathematical Modeling vol. 1, Matfyzpress, Prague, 2007. MR Zbl Available at https://www2.karlin.mff.cuni.cz/~prusv/ncmm/notes/download/product_integration.pdf.
G. Szegö, Über die Randwerte einer analytischen Funktion, Math. Ann. 84 no. 3-4 (1921), 232–244. DOI MR Zbl
N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, I. The regularity condition, Acta Math. 98 (1957), 111–150. DOI MR Zbl
N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes, II. The linear predictor, Acta Math. 99 (1958), 93–137. DOI MR Zbl
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Carlos Kenig
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. The Journal may retract the paper after publication if clear evidence is found that the findings are unreliable as a result of misconduct or honest error.
