Linear Operators: Spectral operators |
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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 ̧ ( R2 , 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 ̧ ( R2 , Σ , ds ) where is the o - field of ...
Page 2042
... integral sign as before , ( 2a à ̧ ̧ ( 0 ) ) ( 9 ) = √ ( −1 ) || 1 Ja ( F - 1μ ) ( s ) q } ° ) ( s ) ds ( To ) ( p ) ... square integrable on RN and the same is true of its Fourier transform F ( ( - 1 ) ( · ) ( · ) ) . The preceding ...
... integral sign as before , ( 2a à ̧ ̧ ( 0 ) ) ( 9 ) = √ ( −1 ) || 1 Ja ( F - 1μ ) ( s ) q } ° ) ( s ) ds ( To ) ( p ) ... square integrable on RN and the same is true of its Fourier transform F ( ( - 1 ) ( · ) ( · ) ) . The preceding ...
Page 2332
... square integrable functions , each vanishing outside an interval of length at most 1 / ẞ , and immediately apply the ordinary theory of orthogonal expansions in Hilbert space ( cf. Theorem IV.4.13 ) to obtain the desired result . If ẞ ...
... square integrable functions , each vanishing outside an interval of length at most 1 / ẞ , and immediately apply the ordinary theory of orthogonal expansions in Hilbert space ( cf. Theorem IV.4.13 ) to obtain the desired result . If ẞ ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero