Spectral analysis of infinite-dimensional Hamiltonian operators / Alatancang Chen, Deyu Wu, Junjie Huang, Guolin Hou.

Format:

Book

Author/Creator:

Chen, Alatancang, author.

Wu, Deyu, 1977- author.

Huang, Junjie, 1977- author.

Hou, Guolin, 1980- author.

Series:

Springer Asia Pacific mathematics series ; v. 5.

Springer Asia Pacific mathematics series, 3091-2563 ; volume 5

Standardized Title:

Wu qiong wei Hamilton suan zi pu fen xi. English

无穷维Hamilton算子谱分析. English

Language:

Chinese

English

Subjects (All):

Hamiltonian systems.

Hamiltonian operator.

Mathematical analysis.

Physical Description:

1 online resource (xix, 303 pages) : illustrations.

Place of Publication:

Singapore : Springer, [2026]

Summary:

This book provides a systematic summary and condensation of research on infinite-dimensional Hamiltonian operator spectrum theory over the past thirty years, and offers simple and concise proofs for some new achievements. The book first introduces Hamiltonian systems, both finite-dimensional and infinite-dimensional, laying the foundation for the subsequent introduction of infinite-dimensional Hamiltonian operator spectrum theory. Chapter 2 presents the infinite-dimensional Hamiltonian operator and systematically elaborates on its spectral properties. Chapters 3 and 4 focus on the completeness of the characteristic function system and the symplectic self-adjointness of infinite-dimensional Hamiltonian operators, respectively, achieving improvements and deepening of the relevant content. Chapters 5 and 6 introduce the numerical range and the theory of indefinite metric spaces related to infinite-dimensional Hamiltonian operators, reflecting the broader application prospects of such operators and the novelty of the book's scope. This book will be useful for senior undergraduate students, graduate students, and teachers specializing in mathematics. To read this book, readers are expected to have knowledge of mathematical analysis and advanced algebra, including matrix theory and some basic knowledge of operator theory.

Contents:

Hamiltonian systems

Spectra of infinite-dimensional Hamiltonian operators

Completeness of eigenvector system of infinite-dimensional Hamiltonian operators

Symplectic self-adjointness of infinite-dimensional Hamiltonian operators

Numerical range theory of infinite-dimensional Hamiltonian operators

Spectral theory of infinite-dimensional Hamiltonian operators in complete indefinite inner product spaces.

Notes:

Translated from the Chinese.

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed April 16, 2026).

Other Format:

Print version: Chen, Alatancang Spectral analysis of infinite-dimensional Hamiltonian operators

ISBN:

9789819521098

9819521092

OCLC:

1586339206

Access Restriction:

Restricted for use by site license