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A Primer on Hilbert Space Theory - Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (Paperback, 2nd ed. 2021)
Loot Price: R1,809
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A Primer on Hilbert Space Theory - Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (Paperback, 2nd ed. 2021)
Series: UNITEXT for Physics
Expected to ship within 10 - 15 working days
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This book offers an essential introduction to the theory of Hilbert
space, a fundamental tool for non-relativistic quantum mechanics.
Linear, topological, metric, and normed spaces are all addressed in
detail, in a rigorous but reader-friendly fashion. The rationale
for providing an introduction to the theory of Hilbert space,
rather than a detailed study of Hilbert space theory itself, lies
in the strenuous mathematics demands that even the simplest
physical cases entail. Graduate courses in physics rarely offer
enough time to cover the theory of Hilbert space and operators, as
well as distribution theory, with sufficient mathematical rigor.
Accordingly, compromises must be found between full rigor and the
practical use of the instruments. Based on one of the authors's
lectures on functional analysis for graduate students in physics,
the book will equip readers to approach Hilbert space and,
subsequently, rigged Hilbert space, with a more practical attitude.
It also includes a brief introduction to topological groups, and to
other mathematical structures akin to Hilbert space. Exercises and
solved problems accompany the main text, offering readers
opportunities to deepen their understanding. The topics and their
presentation have been chosen with the goal of quickly, yet
rigorously and effectively, preparing readers for the intricacies
of Hilbert space. Consequently, some topics, e.g., the Lebesgue
integral, are treated in a somewhat unorthodox manner. The book is
ideally suited for use in upper undergraduate and lower graduate
courses, both in Physics and in Mathematics.
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