On some spectral properties of the weighted ∂¯-Neumann operator

Authors: Berger, Franz, Haslinger, Friedrich

Source: Kyoto J. Math. 59, no. 2 (2019), 441-453

Subject Terms: 32W05, essential spectrum, 35N15, Mathematics - Complex Variables, 32W05 (Primary), 30H20, 35N15 (Secondary), weighted $\overline{\partial}$-Neumann problem, FOS: Mathematics, 47F05, Complex Variables (math.CV), 0101 mathematics, Schrödinger operators, 35P05, 01 natural sciences

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Access URL: http://arxiv.org/pdf/1509.08741
http://arxiv.org/abs/1509.08741
https://projecteuclid.org/journals/kyoto-journal-of-mathematics/volume-59/issue-2/On-some-spectral-properties-of-the-weighted--Neumann-operator/10.1215/21562261-2019-0013.full
https://arxiv.org/abs/1509.08741
https://arxiv.org/pdf/1509.08741.pdf
http://ui.adsabs.harvard.edu/abs/2015arXiv150908741B/abstract
https://projecteuclid.org/euclid.kjm/1556330547

The strong Oka's lemma, bounded plurisubharmonic functions and the $\overline\partial$-Neumann problem

Authors: Harrington, Phillip S., Shaw, Mei-Chi

Source: Asian J. Math. 11, no. 1 (2007), 127-140

Subject Terms: Plurisubharmonic function, 35N15, Oka's lemma, $\overline\partial$-Neumann problem, 32F20, 0101 mathematics, 01 natural sciences

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Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2007/0011/0001/AJM-2007-0011-0001-a012.pdf
https://projecteuclid.org/download/pdf_1/euclid.ajm/1180135555
https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2007/0011/0001/AJM-2007-0011-0001-a012.pdf
https://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0011/0001/a012/
http://projecteuclid.org/euclid.ajm/1180135555

Non‐compactness of the solution operator to $ \bar \partial $ on the Fock‐space in several dimensions: Non-compactness of the solution operator to \(\overline{\partial}\) on the Fock-space in several dimensions

Authors: Georg Schneider

Source: Mathematische Nachrichten. 278:312-317

Subject Terms: 1010 Mathematics, Hankel operator, 1010 Mathematik, \(\overline{\partial}\)-Neumann problem, Bergman spaces of functions in several complex variables, Toeplitz operators, Hankel operators, Wiener-Hopf operators, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, 01 natural sciences, Fock space

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Access URL: https://ucrisportal.univie.ac.at/de/publications/39bfde51-8a6f-4fcb-ae09-3f98fdf99639
https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.200310242

Boundary regularity of admissible operators

Authors: Lampert, C. H.

Source: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Publicacions Matemàtiques; Vol. 49, Núm. 1 (2005); p. 179-195

Subject Terms: Integral operators, integral operators, \(\overline{\partial}\)-Neumann problem, Integral representations, canonical kernels (Szegő, Bergman, etc.), Delta-Neumann-problem, commutator relationship, Commutator relationship

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Access URL: https://ddd.uab.cat/pub/pubmat/02141493v49n1/02141493v49n1p179.pdf
https://ddd.uab.cat/record/2048
http://hdl.handle.net/2072/380060
https://zbmath.org/2186474
https://doi.org/10.5565/publmat_49105_08
http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_49105_08
https://ddd.uab.cat/pub/pubmat/02141493v49n1/02141493v49n1p179.pdf
https://www.dfki.de/web/forschung/publikationen/renameFileForDownload?filename=trecvid.pdf&file_id=uploads_558
https://dialnet.unirioja.es/servlet/articulo?codigo=1294442
https://ddd.uab.cat/record/2048
http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_49105_08

Plurisubharmonic Defining Functions, Good Vector Fields, and Exactness of a Certain One Form: Plurisubharmonic defining functions, good vector fields, and exactness of a certain one form

Authors: Marcel K. Sucheston, Emil J. Straube

Source: Monatshefte f?r Mathematik. 136:249-258

Subject Terms: 32W05, global regularity, Mathematics - Analysis of PDEs, Mathematics - Complex Variables, \(\overline{\partial}\)-Neumann problem, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/pdf/math/0105050v1.pdf
http://arxiv.org/abs/math/0105050
https://zbmath.org/1807907
https://doi.org/10.1007/s006050200044
http://ui.adsabs.harvard.edu/abs/2001math......5050S/abstract
https://link.springer.com/article/10.1007/s006050200044
https://dialnet.unirioja.es/servlet/articulo?codigo=697920
https://link.springer.com/content/pdf/10.1007/s006050200044.pdf

Plurisubharmonic functions and subellipticity of the $\bar\partial$-Neumann problem on non-smooth domains: Plurisubharmonic functions and subellipticity of the \(\bar\partial\)-Neumann problem on non-smooth domains

Authors: Emil J. Straube

Source: Mathematical Research Letters. 4:459-467

Subject Terms: reglarity, \(\overline \partial\)-Neumann problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Plurisubharmonic functions and generalizations, approximation, 01 natural sciences, subelliptic estimate, finite type

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Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1997/0004/0004/MRL-1997-0004-0004-a002.pdf
https://zbmath.org/1082973
https://doi.org/10.4310/mrl.1997.v4.n4.a2
http://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0004/0004/a002/
https://ui.adsabs.harvard.edu/abs/1996math.....12205S/abstract
https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1997/0004/0004/MRL-1997-0004-0004-a002.pdf

Marcinkiewicz multipliers and multi-parameter structure on heisenberg (-type) groups, II: Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. I

Authors: MÜLLER D., RICCI, Fulvio, STEIN E. M.

Source: Mathematische Zeitschrift. 221:267-291

Subject Terms: Analysis on other specific Lie groups, nilpotent Lie groups, Marcinkiewicz multiplier, Marcinkiewicz multipliers, multiparameter, \(L^ p\)-boundedness, \(L^p\)-spaces and other function spaces on groups, semigroups, etc, Multipliers for harmonic analysis in several variables, Heisenberg group, 01 natural sciences, Article, Homomorphisms and multipliers of function spaces on groups, semigroups, etc, \(\overline\partial\)-Neumann problem, 510.mathematics, sublaplacian, Sobolev norm, Heisenberg type groups, fractional integration, \(H\)-type group, 0101 mathematics, \(L_ p\) boundedness

File Description: application/xml; application/pdf; image/jpeg

Access URL: https://zbmath.org/783986
https://doi.org/10.1007/bf01245180
https://zbmath.org/861951
https://doi.org/10.1007/bf02622116
https://rd.springer.com/article/10.1007/BF01245180
https://eudml.org/doc/144254
https://link.springer.com/article/10.1007%2FBF01245180
http://ui.adsabs.harvard.edu/abs/1995InMat.119..199M/abstract
https://link.springer.com/content/pdf/10.1007/BF02622116.pdf
https://link.springer.com/article/10.1007/BF02622116
https://eudml.org/doc/174850
https://hdl.handle.net/11384/399
https://hdl.handle.net/11384/587

Singular Integrals Related to the Radon Transform and Boundary Value Problems

Authors: Phong, D. H., Stein, E. M.

Source: Proceedings of the National Academy of Sciences of the United States of America, 1983 Dec . 80(24), 7697-7701.

Access URL: https://www.jstor.org/stable/23221

Small Sets of Infinite Type are Benign for the $\overline\partial$-Neumann Problem

Authors: Boas, Harold P.

Source: Proceedings of the American Mathematical Society, 1988 Jun 01. 103(2), 569-578.

Access URL: https://www.jstor.org/stable/2047181

Estimates on the Bergman Kernels of Convex Domains: Estimates on the Bergman kernels of convex domains

Authors: J.D. Mcneal

Source: Advances in Mathematics. 109:108-139

Subject Terms: Mathematics(all), convex domain, Integral representations, canonical kernels (Szegő, Bergman, etc.), \(\overline \partial\)-Neumann problem, Pseudoconvex domains, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Bergman kernel, 01 natural sciences, pseudoconvex

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Access URL: https://zbmath.org/710357
https://doi.org/10.1006/aima.1994.1082
https://www.sciencedirect.com/science/article/pii/S0001870884710826
https://core.ac.uk/display/82440915

De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the $$\bar \partial - Neumann$$ problem: De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the \(\bar \partial\)-Neumann problem

Authors: Harold P. Boas, Emil J. Straube

Source: Journal of Geometric Analysis. 3:225-235

Subject Terms: \(\overline \partial\)-Neumann problem, de Rham cohomology, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Sobolev space, 01 natural sciences, de Rham theory in global analysis

File Description: application/xml

Access URL: https://zbmath.org/425631
https://doi.org/10.1007/bf02921391
https://link.springer.com/content/pdf/10.1007/BF02921391.pdf
https://link.springer.com/article/10.1007%2FBF02921391

Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results

Authors: Klas Diederich, Gregor Herbort

Source: Journal of Geometric Analysis. 3:237-267

Subject Terms: Bergman metric, Pseudoconvex domains, Bergman kernel, pseudoconvex domains, pseudoconvex extendability, 01 natural sciences, \(\overline\partial\)-Neumann problem, local analytic invariants, Integral representations, canonical kernels (Szegő, Bergman, etc.), multitype, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, local geometric invariants, Invariant metrics and pseudodistances in several complex variables, finite type

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF02921392

Compactness for the $${\overline{\partial}}$$-Neumann problem: a functional analysis approach

Authors: Haslinger, Friedrich

Source: Collectanea mathematica. May 2011 62(2):121-129

Analysis and Geometry on Worm Domains

Authors: Krantz, Steven G., Peloso, Marco M.

Source: Journal of Geometric Analysis. April 2008 18(2):478-510

Sufficient Conditions for Subellipticity on Weakly Pseudo-Convex Domains

Authors: Kohn, J. J.

Source: Proceedings of the National Academy of Sciences of the United States of America, 1977 Jun 01. 74(6), 2214-2216.

Access URL: https://www.jstor.org/stable/66798

Singularity and regularity -- local and global

Authors: Christ, Michael

Source: Proceedings of the International Congress of Mathematicians 1998 ISBN: 9783985470457

Subject Terms: global regularity, Harmonic analysis in several variables, hypoellipticity, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Bergman projection, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann problem

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Access URL: https://zbmath.org/1184297

COMPLEX ANALYSIS IN ONE AND SEVERAL VARIABLES: Complex analysis in one and several variables

Authors: Chen, So-Chin

Source: Taiwanese J. Math. 4, no. 4 (2000), 531-568

Subject Terms: Research exposition (monographs, survey articles) pertaining to functions of a complex variable, domain of holomorphy, pseudoconvexity, \(\overline{\partial}\)-Neuman problem, 01 natural sciences, $\overline\partial$-Neumann problem, 32-02, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, 0103 physical sciences, Domains of holomorphy, Bergman projection, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, condition $R$, condition \(R\)

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Access URL: https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume-4/issue-4/COMPLEX-ANALYSIS-IN-ONE-AND-SEVERAL-VARIABLES/10.11650/twjm/1500407292.full
http://site.iugaza.edu.ps/fshoga/files/2010/02/COMPLEX_ANALYSIS_IN_ONE_AND_SEVERAL_VARIABLES.pdf
https://projecteuclid.org/download/pdf_1/euclid.twjm/1500407292
http://projecteuclid.org/euclid.twjm/1500407292

The $\overline\partial$-Neumann problem in the Sobolev topology: The \(\overline\partial\)-Neumann problem in the Sobolev topology

Authors: FONTANA, LUIGI, Krantz, SG, Peloso, MM

Subject Terms: Hypoelliptic equations, boundary value problem, Neumann problem, Pseudoconvex domains, Other notions of convexity in relation to several complex variables, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, modified \(\overline\partial\)-Neumann problem

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Access URL: https://zbmath.org/1366161
https://hdl.handle.net/10281/17818

Global regularity of the $$\bar \partial $$ -Neumann problem on circular domains: Global regularity of the \(\overline{\partial}\)-Neumann problem on circular domains

Authors: So-Chin Chen

Source: Mathematische Annalen. 285:1-12

Subject Terms: Reinhardt pseudoconvex domain, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), 0103 physical sciences, Pseudoconvex domains, global regularity of the \(\overline{\partial }\)-Neumann problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, pseudoconvex circular domain, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/4081958
https://doi.org/10.1007/bf01442668
https://eudml.org/doc/164581
https://link.springer.com/article/10.1007%2FBF01442668

Semi-global analyticity for the \(\overline{\partial}\)-Neumann problem in pseudo-convex domains

Authors: Ben Moussa, Benoît

Subject Terms: \(\overline\partial\) Neumann problem, Pseudoconvex domains, Analytical consequences of geometric convexity (vanishing theorems, etc.), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, pseudoconvex domains

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Access URL: https://zbmath.org/1467772