Linear Operators, Part 2 |
From inside the book
Results 1-3 of 6
Page 1983
... square integrable functions on real Euclidean space RN of N dimensions . We shall show that this algebra of all ... integral , is a B * -algebra which is * -equivalent to the B * -algebra  = L ( RN , Σ , ds ) where is the o - field of ...
... square integrable functions on real Euclidean space RN of N dimensions . We shall show that this algebra of all ... integral , is a B * -algebra which is * -equivalent to the B * -algebra  = L ( RN , Σ , ds ) where is the o - field of ...
Page 2042
... integral sign as before , -1 . ( ¿ aà ̧ ̧ ( 0 ) ) ( q ) = √ ̧ ̧ ( −1 ) | a¦1 ĉa ( F − 1μ ) ( s ) q¦o ' ( s ) ds ... square integrable on RN and the same is true of its Fourier transform F ( ( — 1 ) || 1 ( i · ) a§o ( · ) ) . The ...
... integral sign as before , -1 . ( ¿ aà ̧ ̧ ( 0 ) ) ( q ) = √ ̧ ̧ ( −1 ) | a¦1 ĉa ( F − 1μ ) ( s ) q¦o ' ( s ) ds ... square integrable on RN and the same is true of its Fourier transform F ( ( — 1 ) || 1 ( i · ) a§o ( · ) ) . The ...
Page 2332
... square integrable functions , each vanishing outside an interval of length at most 1/8 , and immediately apply the ordinary theory of orthogonal expansions in Hilbert space ( cf. Theorem IV.4.13 ) to obtain the desired result . If B - R ...
... square integrable functions , each vanishing outside an interval of length at most 1/8 , and immediately apply the ordinary theory of orthogonal expansions in Hilbert space ( cf. Theorem IV.4.13 ) to obtain the desired result . If B - R ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero