naa a22 4500 510810918 CHVBK 20180411083442.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9303-7 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9303-7 Fundamental Solutions to □ b on Certain Quadrics [Elektronische Daten] [Albert Boggess, Andrew Raich] The purpose of this article is to expand the number of examples for which the complex Green operator, that is, the fundamental solution to the Kohn Laplacian, can be computed. We use the Lie group structure of quadric submanifolds of ℂ n ×ℂ m and the group Fourier transform to reduce the □ b equation to ones that can be solved using modified Hermite functions. We use Mehler's formula and investigate (1)quadric hypersurfaces, where the eigenvalues of the Levi form are not identical (including possibly zero eigenvalues), and (2)the canonical quadrics in ℂ4 of codimension two. Mathematica Josephina, Inc., 2012 Kohn Laplacian nationallicence Complex Green operator nationallicence Lie group nationallicence Quadrics nationallicence Heisenberg group nationallicence Fundamental solution nationallicence Boggess Albert Department of Mathematics, Texas A&M University, Mailstop 3368, 77845-3368, College Station, TX, USA aut Raich Andrew Department of Mathematical Sciences, 1 University of Arkansas, SCEN 327, 72701, Fayetteville, AR, USA aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1729-1752 1050-6926 23:4<1729 2013 23 12220 https://doi.org/10.1007/s12220-012-9303-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9303-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boggess Albert Department of Mathematics, Texas A&M University, Mailstop 3368, 77845-3368, College Station, TX, USA aut NATIONALLICENCE 700 1- Raich Andrew Department of Mathematical Sciences, 1 University of Arkansas, SCEN 327, 72701, Fayetteville, AR, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1729-1752 1050-6926 23:4<1729 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer