FUNCTIONAL ANALYSIS
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FUNCTIONAL ANALYSIS
Entering Hilbert Space
by Vagn Lundsgaard Hansen (Technical University of Denmark, Denmark)
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of H�lder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.
Contents:
- Basic Elements of Metric Topology
- New Types of Function Spaces
- Theory of Hilbert Spaces
- Operators on Hilbert Spaces
- Spectral Theory
- Exercises and Applications
View Full Text (4,726 KB)
Readership: Undergraduates in mathematical and physical sciences, and electrical and electronic engineering.
"This is a well-written student-friendly basic introduction to functional analysis and Hilbert space ..."
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148pp
Pub. date: May 2006
eISBN 978-981-277-459-0
Price: US$62
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