Revista de la
Unión Matemática Argentina
Remarks on a boundary value problem for a matrix valued $\overline{\partial}$ equation
Carlos E. Kenig
Volume 66, no. 1 (2023), pp. 207–211    

https://doi.org/10.33044/revuma.4326

Download PDF

Abstract

In this short note, we discuss a boundary value problem for a matrix valued $\overline{\partial}$ equation.

References

  1. 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.
  2. M. S. Brodskiĭ, Triangular and Jordan representations of linear operators, Translations of Mathematical Monographs, Vol. 32, American Mathematical Society, Providence, RI, 1971.  MR
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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.
  8. A. Logunov, E. Malinnikova, N. Nadirashvili, and F. Nazarov, The Landis conjecture on exponential decay, 2020. arXiv 2007.07034 [math.AP].
  9. V. P. Potapov, The multiplicative structure of $J$-contractive matrix functions, Amer. Math. Soc. Transl. (2) 15 (1960), 131–243.  DOI  MR
  10. 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.
  11. 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.
  12. G. Szegö, Über die Randwerte einer analytischen Funktion, Math. Ann. 84 no. 3-4 (1921), 232–244.  DOI  MR  Zbl
  13. 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
  14. 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