東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Convolution Operators on Euclidean and Symmetric Spaces = = 欧氏空间与对称空间上的卷积算子.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convolution Operators on Euclidean and Symmetric Spaces =/
其他題名:	欧氏空间与对称空间上的卷积算子.
作者:	Wang, Jue.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	171 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-09, Section: B.
Contained By:	Dissertations Abstracts International83-09B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28963531
ISBN:	9798206396652

Convolution Operators on Euclidean and Symmetric Spaces = = 欧氏空间与对称空间上的卷积算子.
Wang, Jue.

Convolution Operators on Euclidean and Symmetric Spaces =欧氏空间与对称空间上的卷积算子. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 171 p.

Source: Dissertations Abstracts International, Volume: 83-09, Section: B.

Thesis (Ph.D.)--Tufts University, 2022.

This item must not be sold to any third party vendors.

In the 1960s, L. Ehrenpreis established some classical results on the surjectivity of convolution operators on Euclidean spaces, including the existence of fundamental solutions. These results generalize the well-known Malgrange-Ehrenpreis Theorem. In this thesis, we first discuss some applications of Ehrenpreis' classical results. In particular, we obtain an explicit formula for the "snapshot" problem of the wave equation.After that, we extend Ehrenpreis' results from Euclidean spaces to noncompact symmetric spaces. We consider the right convolution operator cμ, where the convolution kernel μ is a compactly supported distribution. Precisely, we give a concrete condition for μ which holds if and only if cμ has a fundamental solution and is surjective on various spaces of functions or distributions. A corollary of our results is the Malgrange-Ehrenpreis Theorem on noncompact symmetric spaces, a classical result established by Helgason in 1964.Finally, we establish generalizations of Asgeirsson's Mean Value Theorem (AsMVT) on Euclidean spaces, noncompact rank-one symmetric spaces, and compact symmetric spaces, where the last one is our main result. The original AsMVT gives a mean value relation satisfied by smooth solutions of the ultrahyperbolic equation on Euclidean spaces. In our generalized AsMVT, the mean value relation is generalized to a convolution relation. Our results also extend Helgason's work about AsMVT on rank-one symmetric spaces.

ISBN: 9798206396652Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Asgeirsson's mean value theorem

Convolution Operators on Euclidean and Symmetric Spaces = = 欧氏空间与对称空间上的卷积算子.
LDR:02709nmm a2200373 4500 001 2346926
005 20220706051325.5
008 241004s2022 ||||||||||||||||| ||eng d
020 $a 9798206396652
035 $a (MiAaPQ)AAI28963531
035 $a AAI28963531
040 $a MiAaPQ $c MiAaPQ
100 1 $a Wang, Jue. $3 1272234
245 1 0 $a Convolution Operators on Euclidean and Symmetric Spaces = $b 欧氏空间与对称空间上的卷积算子.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 171 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-09, Section: B.
500 $a Advisor: Gonzalez, Fulton B.
502 $a Thesis (Ph.D.)--Tufts University, 2022.
506 $a This item must not be sold to any third party vendors.
520 $a In the 1960s, L. Ehrenpreis established some classical results on the surjectivity of convolution operators on Euclidean spaces, including the existence of fundamental solutions. These results generalize the well-known Malgrange-Ehrenpreis Theorem. In this thesis, we first discuss some applications of Ehrenpreis' classical results. In particular, we obtain an explicit formula for the "snapshot" problem of the wave equation.After that, we extend Ehrenpreis' results from Euclidean spaces to noncompact symmetric spaces. We consider the right convolution operator cμ, where the convolution kernel μ is a compactly supported distribution. Precisely, we give a concrete condition for μ which holds if and only if cμ has a fundamental solution and is surjective on various spaces of functions or distributions. A corollary of our results is the Malgrange-Ehrenpreis Theorem on noncompact symmetric spaces, a classical result established by Helgason in 1964.Finally, we establish generalizations of Asgeirsson's Mean Value Theorem (AsMVT) on Euclidean spaces, noncompact rank-one symmetric spaces, and compact symmetric spaces, where the last one is our main result. The original AsMVT gives a mean value relation satisfied by smooth solutions of the ultrahyperbolic equation on Euclidean spaces. In our generalized AsMVT, the mean value relation is generalized to a convolution relation. Our results also extend Helgason's work about AsMVT on rank-one symmetric spaces.
590 $a School code: 0234.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Asgeirsson's mean value theorem
653 $a Convolution operator
653 $a Fundamental solution
653 $a Malgrange-ehrenpreis theorem
653 $a Surjectivity
653 $a Symmetric space
690 $a 0405
690 $a 0642
710 2 $a Tufts University. $b Mathematics. $3 1058738
773 0 $t Dissertations Abstracts International $g 83-09B.
790 $a 0234
791 $a Ph.D.
792 $a 2022
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28963531