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Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
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A Primer on Hilbert Space Theory - Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (Paperback, Softcover reprint of the original 1st ed. 2015)
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A Primer on Hilbert Space Theory - Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (Paperback, Softcover reprint of the original 1st ed. 2015)
Series: UNITEXT for Physics
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This book is an 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 an
introduction to the theory of Hilbert space, rather than a detailed
study of Hilbert space theory itself, resides in the very high
mathematical difficulty of even the simplest physical case. Within
an ordinary graduate course in physics there is insufficient time
to cover the theory of Hilbert spaces and operators, as well as
distribution theory, with sufficient mathematical rigor.
Compromises must be found between full rigor and practical use of
the instruments. The book is based on the author's lessons on
functional analysis for graduate students in physics. It will equip
the reader to approach Hilbert space and, subsequently, rigged
Hilbert space, with a more practical attitude. With respect to the
original lectures, the mathematical flavor in all subjects has been
enriched. Moreover, a brief introduction to topological groups has
been added in addition to exercises and solved problems throughout
the text. With these improvements, the book can be used in upper
undergraduate and lower graduate courses, both in Physics and in
Mathematics.
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