Applications of Functional Analysis and Operator TheoryFunctional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.
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Contents
| 1 | |
| 39 | |
Chapter 3 Foundations of Linear Operator Theory | 65 |
Chapter 4 Introduction to Nonlinear Operators | 115 |
Chapter 5 Compact Sets in Banach Spaces | 147 |
Chapter 6 The Adjoint Operator | 157 |
Chapter 7 Linear Compact Operators | 189 |
Chapter 8 Nonlinear Compact Operators and Monotonicity | 217 |
Chapter 11 Linear Elliptic Partial Differential Equations | 303 |
Chapter 12 The Finite Element Method | 343 |
Chapter 13 Introduction to Degree Theory | 359 |
Chapter 14 Bifurcation Theory | 385 |
| 409 | |
List of Symbols | 417 |
| 421 | |
Mathematics in Science and Engineering | 427 |
Chapter 9 The Spectral Theorem | 241 |
Chapter 10 Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations | 269 |
Other editions - View all
Applications of Functional Analysis and Operator Theory V. Hutson,John Sydney Pym No preview available - 1980 |
Common terms and phrases
adjoint analysis applications approximation argument assume ball Banach space bounded called Chapter closed compact complex condition consider constructed contained convergent corresponding deduce defined Definition denoted dense derivative differential equation difficulties dimensions discussion domain easy eigenfunctions eigenvalue element equation equivalent Example existence extension fact finite dimensional fixed point follows formal functions further given gives Hence Hilbert space hold important independent inequality infinite integral equation interval known Lemma limit linear operator linear subspace Mapping measure method monotone natural needed non-negative nonlinear obtained obvious positive possible problem Proof properties prove relation relatively respectively restriction result Riemann integral satisfies self-adjoint operator sense sequence side simple solution spectrum subset sup norm Suppose Theorem theory unique valued vector space zero
Popular passages
Page ii - This is volume 199 in MATHEMATICS IN SCIENCE AND ENGINEERING Edited by CK Chui, Stanford University A list of recent titles in this series appears at the end of this volume.
Page 36 - In a normed vector space show that the union of any class of open sets is open, and the intersection of a finite number of open sets is open.
Page 7 - The method used adopts a rather neat device for achieving this calculation and this will be discussed in the next section. It should be noted that...
Page 36 - Prove also that the intersection of any class of closed sets is closed, and that the union of a finite number of closed sets is closed.
Page 36 - It is easy to show that an open ball is an open set and a closed ball is a closed set. If x € M, we refer to any open set S containing x as an open neighborhood of x.
Page 4 - ... S is said to be linearly independent. An arbitrary set S of vectors in V is linearly independent iff every finite non-empty subset of S is linearly independent; otherwise it is linearly dependent. If there is a positive integer n such that V contains n but not n + 1 linearly independent vectors, V is said to be finite dimensional with dimension n. V is infinite dimensional iff it is not finite dimensional. The finite set S of vectors in V is called a basis of V iff S is linearly independent and...