An Introduction to Classical and P-adic Theory of Linear Operators and Applications

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Nova Publishers, 2006 - Mathematics - 116 pages
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This book provides the reader with a self-contained treatment of the classical operator theory with significant applications to abstract differential equations, and an elegant introduction to basic concepts and methods of the rapidly growing theory of the so-called p-adic operator theory.
 

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Contents

Banach and Hilbert Spaces
1
113 Examples of Banach Spaces
3
12 Hilbert Spaces
6
122 Hilbert Spaces
7
123 Projections
8
13 Bibliographical Notes
10
Bounded Linear Operators on Classical and padic Hilbert Spaces
11
212 The Adjoint of An Operator
14
317 Maximal Linear Operators
59
318 Algebraic Sum of Linear Operators
60
323 Unbounded Linear Operators On Ew
65
33 Closed Linear Operators on Ew
67
34 The Diagonal Operator on E
68
35 The Equation Ax yon Eo
71
352 Application to the Perturbation of Bases on Ew
72
353 The Unbounded Case
73

213 The Inverse of An Operator
15
214 Normal and Selfadjoint Operators
17
215 Square Root of a Positive Selfadjoint Operator
18
216 Compact Operators
20
217 HilbertSchmidt Operators
22
22 Bounded Linear Operators on padic Hilbert Spaces Ew
24
223 Ultrametric Banach Spaces
27
224 Free Banach Spaces
28
225 The padic Hilbert Space Ew
29
226 Bounded Linear Operators E
31
23 padic HilbertSchmidt Operators
35
233 Further Properties of HilbertSchmidt Operators on Ew
39
234 Applications
43
24 Bibliographical Notes
46
Unbounded Linear Operators on Classical and padic Hilbert Spaces
47
312 Closed and Closable Linear Operators
49
313 Invariant Subspaces for Unbounded Linear Operators
51
314 Semigroups of Linear Operators
53
315 Spectral Theory for Unbounded Linear Operators
55
316 Symmetric and Selfadjoint Linear Operators
56
36 Bibliographical Notes
75
Almost Automorphic and Almost Periodic Solutions to Differential Equations
77
42 Basic Definitions and Notations
78
422 Almost Periodic Functions
82
43 The Equation ut Aut +But +ft
83
432 Almost Periodic Mild Solutions
85
44 The Method of Invariant Subspaces for Unbounded Linear Operators
87
443 Applications to Some SecondOrder Differential Equations
90
444 Almost Automorphic Solutions to Some SecondOrder Hyperbolic Equations
91
45 Pseudo Almost Periodic Solutions to Some SecondOrder Differential Equations
95
452 Applications
98
46 Existence and Uniqueness of Almost Automorphic Mild Solutions to Semilinear Equations
100
462 Existence and Uniqueness of Mild Solutions
101
463 Case of Bounded Perturbations
104
464 Applications
105
47 Bibliographical Notes
108
References
109
Index
115
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