Functional Analysis with a Historical Perspective
Basic Topics
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Beschreibung
This core textbook on functional analysis is intended for senior undergraduates and graduate mathematics students. It is suitable for both classrooms and for self-study. The first in a two-volume series presents all the basic material needed for a solid foundation in the subject. It opens with a concise overview of the historical evolution of the subject and goes on to present foundational material in a clear, succinct manner, integrating original source quotes to enrich the narrative and blending the historical perspectives harmoniously with the flow of the subject. Pedagogically, the short chapters are more conducive for learning, and each chapter concludes with applications (including some unusual ones) to diverse fields and exercises to hone students’ understanding. The applications can also serve as sources for student seminars. Various formulations of the spectral theorem and their equivalence are discussed. Different approaches to some important results are presented to enrich the toolkit of the students. The style is neither terse nor verbose, requiring occasional paper-pencil work from the reader. The bibliography is rich and includes all the original works of the founding fathers. Thumbnail biographies of the mathematicians involved should pep up the readers.
This core textbook on functional analysis is intended for senior undergraduates and graduate mathematics students. It is suitable for both classrooms and for self-study. The first in a two-volume series presents all the basic material needed for a solid foundation in the subject. It opens with a concise overview of the historical evolution of the subject and goes on to present foundational material in a clear, succinct manner, integrating original source quotes to enrich the narrative and blending the historical perspectives harmoniously with the flow of the subject. Pedagogically, the short chapters are more conducive for learning, and each chapter concludes with applications (including some unusual ones) to diverse fields and exercises to hone students’ understanding. The applications can also serve as sources for student seminars. Various formulations of the spectral theorem and their equivalence are discussed. Different approaches to some important results are presented to enrich the toolkit of the students. The style is neither terse nor verbose, requiring occasional paper-pencil work from the reader. The bibliography is rich and includes all the original works of the founding fathers. Thumbnail biographies of the mathematicians involved should pep up the readers.
Presents a core text in functional analysis and includes a historical perspective of the subject Offers shorter chapters with applications to diverse fields and exercises to hone students’ understanding Introduces different formulations and various approaches to the spectral theorem to enrich the toolkit of the readers
Autor*in
Parthasarathy Krishnan
Themen in »Functional Analysis with a Historical Perspective«
functional analysis operator theory Fourier analysis Banach algebras operator algebras geometry of Banach spaces Gabor frames