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Integral Operators in the Complex Domain and Analytic Regularity for Differential Operators of Principal Type
Integral Operators in the Complex Domain and Analytic Regularity for Differential Operators of Principal Type
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105639
- ISBN
- 9798265478375
- DDC
- 510
- 서명/저자
- Integral Operators in the Complex Domain and Analytic Regularity for Differential Operators of Principal Type
- 발행사항
- [Sl] : University of California, Los Angeles, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 111 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-06, Section: B.
- 주기사항
- Advisor: Khitrik, Mikhail.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Los Angeles, 2025.
- 초록/해제
- 요약This dissertation has three parts. In the first part, we characterize boundedness and compactness of pullback operators under holomorphic maps between Bargmann spaces of entire holomorphic functions with quadratic strictly plurisubharmonic exponential weights, extending the result of [CaMcSc03], obtained in the case of the radial quadratic weight. We also show that the pullback operator between Bargmann spaces is compact precisely when it is of trace class, with sub-exponentially decaying singular values. In the second part, we study pseudodifferential operators associated to microlocally defined normed symbol spaces of limited regularity, introduced by J. Sjostrand [Sj08]. Extending the results of [Sj08], boundedness of such operators on modulation spaces is obtained under suitable conditions, and continuity properties of the Weyl composition product are established. Finally, in the third part, we obtain microlocal analytic regularity at characteristic points for semiclassical differential operators with analytic coefficients on the real line, under suitable assumptions on higher order Poisson brackets of the real and imaginary parts of the principal symbol at those points.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 일반주제명
- Computational physics
- 키워드
- Radial quadratic
- 기타저자
- University of California, Los Angeles Mathematics 0540
- 기본자료저록
- Dissertations Abstracts International. 87-06B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798265478375
■035 ▼a(MiAaPQ)AAI32395779
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aJohnson, Reid Camden.
■24510▼aIntegral Operators in the Complex Domain and Analytic Regularity for Differential Operators of Principal Type
■260 ▼a[Sl]▼bUniversity of California, Los Angeles▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a111 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-06, Section: B.
■500 ▼aAdvisor: Khitrik, Mikhail.
■5021 ▼aThesis (Ph.D.)--University of California, Los Angeles, 2025.
■520 ▼aThis dissertation has three parts. In the first part, we characterize boundedness and compactness of pullback operators under holomorphic maps between Bargmann spaces of entire holomorphic functions with quadratic strictly plurisubharmonic exponential weights, extending the result of [CaMcSc03], obtained in the case of the radial quadratic weight. We also show that the pullback operator between Bargmann spaces is compact precisely when it is of trace class, with sub-exponentially decaying singular values. In the second part, we study pseudodifferential operators associated to microlocally defined normed symbol spaces of limited regularity, introduced by J. Sjostrand [Sj08]. Extending the results of [Sj08], boundedness of such operators on modulation spaces is obtained under suitable conditions, and continuity properties of the Weyl composition product are established. Finally, in the third part, we obtain microlocal analytic regularity at characteristic points for semiclassical differential operators with analytic coefficients on the real line, under suitable assumptions on higher order Poisson brackets of the real and imaginary parts of the principal symbol at those points.
■590 ▼aSchool code: 0031.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■650 4▼aComputational physics
■653 ▼aIntegral operators
■653 ▼aAnalytic regularity
■653 ▼aRadial quadratic
■653 ▼aSemiclassical differential operators
■690 ▼a0405
■690 ▼a0216
■690 ▼a0364
■71020▼aUniversity of California, Los Angeles▼bMathematics 0540.
■7730 ▼tDissertations Abstracts International▼g87-06B.
■790 ▼a0031
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17360921▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
