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Euclidean spherical harmonics and th...

Shakarchi, Rami.

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Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels./
Author:	Shakarchi, Rami.
Description:	221 p.
Notes:	Adviser: Charles L. Fefferman.
Contained By:	Dissertation Abstracts International63-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3041866
ISBN:	0493553606

Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels.
Shakarchi, Rami.

Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels. - 221 p.

Adviser: Charles L. Fefferman.

Thesis (Ph.D.)--Princeton University, 2002.

In addition, various other mapping properties of the kernels <italic> K<super>p,q</super></italic> are investigated. We also deduce a formula for the Green's function for spherical functions on the Heisenberg ball.

ISBN: 0493553606Subjects--Topical Terms:

515831
Mathematics.

Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels.
LDR:02626nam 2200301 a 45 001 935986
005 20110510
008 110510s2002 eng d
020 $a 0493553606
035 $a (UnM)AAI3041866
035 $a AAI3041866
040 $a UnM $c UnM
100 1 $a Shakarchi, Rami. $3 719417
245 1 0 $a Euclidean spherical harmonics and the Heisenberg Laplacian: A new family of kernels.
300 $a 221 p.
500 $a Adviser: Charles L. Fefferman.
500 $a Source: Dissertation Abstracts International, Volume: 63-02, Section: B, page: 0833.
502 $a Thesis (Ph.D.)--Princeton University, 2002.
520 $a In addition, various other mapping properties of the kernels <italic> K<super>p,q</super></italic> are investigated. We also deduce a formula for the Green's function for spherical functions on the Heisenberg ball.
520 $a This work investigates the use of Euclidean spherical harmonics in the context of boundary value problems for the Laplacian <math> <f> <sc>L</sc></f> </math> on the Heisenberg group of dimension five. We express the <math> <f> <a><ac><g>6</g></ac><ac>&d1;</ac></a><inf>b</inf></f> </math>-Neumann boundary conditions on the Heisenberg ball as an infinite number of two-dimensional systems.
520 $a We then invert the Folland-Stein fundamental solution to obtain a family of kernels <italic>K<super>p,q</super></italic> indexed by the bi-degree of spherical harmonics. These kernels are fundamental solutions for the operators <italic> L<super>p,q</super></italic> obtained by restricting <math> <f> <sc>L</sc></f> </math> on an appropriate space of functions.
520 $a Finally, we establish the Fredholm property on a weighted <italic>L</italic><super> 2</super> space of the first layer potentials induced by these kernels. This is done by “regularizing” <italic>K<super>p,q</super></italic>, that is, obtaining an operator <italic>R<super>p,q</super></italic> so that <display-math> <fd> <fl>Rp,qKp,q=I+<rm>compact<hsp sp="1.000"> <hsp sp="0.265">and<hsp sp="1.000"><hsp sp="0.265"><mit>K p<rm>,<mit>q</mit></rm>Rp<rm>,<mit>q</mit></rm> <rm>=<mit>I<hsp sp="0.167"><rm>+compact.</rm></mit></rm></mit> </rm></fl> </fd> </display-math>Finding the <italic>R<super>p,q</super></italic>s amounts to the inversion of symbols arising from Mellin operators.
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 63-02B.
790 $a 0181
790 1 0 $a Fefferman, Charles L., $e advisor
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3041866