Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1985
... transform Fp of a function & in Ĝ is given by the integral 1 ( 4 ) ( Fq ) ( s ) = ( 2π ) N / 2 S e - istq ( t ) dt , SЄ RN . RN The basic inversion formula for this integral is due to Fourier and is contained in the following theorem ...
... transform Fp of a function & in Ĝ is given by the integral 1 ( 4 ) ( Fq ) ( s ) = ( 2π ) N / 2 S e - istq ( t ) dt , SЄ RN . RN The basic inversion formula for this integral is due to Fourier and is contained in the following theorem ...
Page 2000
... transform ( 34 ) is in 2 and has ( 35 ) p ( t ) dt , 9 € H , ( hq ) ( s ) = 1.i.m.s - t > e 8 - t 0 + 3 = πT . h = - -Ti [ _sgn s e ( ds ) , | h | = 16 EXAMPLE ( Calderón and Zygmund ) . An analogue of the Hilbert transform in case the ...
... transform ( 34 ) is in 2 and has ( 35 ) p ( t ) dt , 9 € H , ( hq ) ( s ) = 1.i.m.s - t > e 8 - t 0 + 3 = πT . h = - -Ti [ _sgn s e ( ds ) , | h | = 16 EXAMPLE ( Calderón and Zygmund ) . An analogue of the Hilbert transform in case the ...
Page 2483
... transformation z → Sz + az in the space l , is similar to the transformation S. ai.i 8 Let S , A , lp , and so on , be as in Exercises 5 , 6 , and 7. Show that ( a ) If a ɛ A is purely subdiagonal , that is , if the matrix elements of ...
... transformation z → Sz + az in the space l , is similar to the transformation S. ai.i 8 Let S , A , lp , and so on , be as in Exercises 5 , 6 , and 7. Show that ( a ) If a ɛ A is purely subdiagonal , that is , if the matrix elements of ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero