國立高雄大學圖資館 |

Language: English

Back

Geometric harmonic analysis.III,Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric harmonic analysis.by Dorina Mitrea, Irina Mitrea, Marius Mitrea.
remainder title:	Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering
Author:	Mitrea, Dorina.
other author:	Mitrea, Irina.
Published:	Cham :Springer International Publishing :2023.
Description:	1 online resource (xvii, 972 p.) :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Divergence theorem.
Online resource:	https://doi.org/10.1007/978-3-031-22735-6
ISBN:	9783031227356$q(electronic bk.)

Geometric harmonic analysis.III,Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering
Mitrea, Dorina.

Geometric harmonic analysis.III,Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering[electronic resource] /Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scatteringby Dorina Mitrea, Irina Mitrea, Marius Mitrea. - Cham :Springer International Publishing :2023. - 1 online resource (xvii, 972 p.) :ill., digital ;24 cm. - Developments in mathematics,v. 7742197-795X ;. - Developments in mathematics ;v.25..

Introduction and Statement of Main Results Concerning the Divergence Theorem -- Examples, Counterexamples, and Additional Perspectives -- Tools from Geometric Measure Theory, Harmonic Analysis, and functional Analysis -- Open Sets with Locally Finite Surface Measures and Boundary Behavior -- Proofs of the Main Results Pertaining to the Divergence Theorem -- Applications to Singular Integrals, Function Spaces, Boundary Problems, and Further Results.

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.

ISBN: 9783031227356$q(electronic bk.)

Standard No.: 10.1007/978-3-031-22735-6doiSubjects--Topical Terms:

669000
Divergence theorem.

LC Class. No.: QA433

Dewey Class. No.: 515.4

Geometric harmonic analysis.III,Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering
LDR:02738nmm a2200349 a 4500 001 638055
003 DE-He213
005 20230512112630.0
006 m d
007 cr nn 008maaau
008 230921s2023 sz s 0 eng d
020 $a 9783031227356$q(electronic bk.)
020 $a 9783031227349$q(paper)
024 7 $a 10.1007/978-3-031-22735-6 $2 doi
035 $a 978-3-031-22735-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA433
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 515.4 $2 23
090 $a QA433 $b .M684 2023
100 1 $a Mitrea, Dorina. $3 825961
245 1 0 $a Geometric harmonic analysis. $n III, $p Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering $h [electronic resource] / $c by Dorina Mitrea, Irina Mitrea, Marius Mitrea.
246 3 0 $a Integral representations, Calderon-Zygmund theory, Fatou theorems, and applications to scattering
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a 1 online resource (xvii, 972 p.) : $b ill., digital ; $c 24 cm.
490 1 $a Developments in mathematics, $x 2197-795X ; $v v. 774
505 0 $a Introduction and Statement of Main Results Concerning the Divergence Theorem -- Examples, Counterexamples, and Additional Perspectives -- Tools from Geometric Measure Theory, Harmonic Analysis, and functional Analysis -- Open Sets with Locally Finite Surface Measures and Boundary Behavior -- Proofs of the Main Results Pertaining to the Divergence Theorem -- Applications to Singular Integrals, Function Spaces, Boundary Problems, and Further Results.
520 $a This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.
650 0 $a Divergence theorem. $3 669000
650 0 $a Geometric measure theory. $3 309750
650 1 4 $a Integral Transforms and Operational Calculus. $3 913382
700 1 $a Mitrea, Irina. $3 939432
700 1 $a Mitrea, Marius. $3 726906
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Developments in mathematics ; $v v.25. $3 558834
856 4 0 $u https://doi.org/10.1007/978-3-031-22735-6
950 $a Mathematics and Statistics (SpringerNature-11649)