Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1154
... constant c , ( R ( 2 ) , Σ ( 2 ) , λ ( 2 ) ) = c ( R , E , 2 ) × ( R , Σ , λ ) . Since it is clear that ( 2 ) ExE ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
... constant c , ( R ( 2 ) , Σ ( 2 ) , λ ( 2 ) ) = c ( R , E , 2 ) × ( R , Σ , λ ) . Since it is clear that ( 2 ) ExE ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
Page 1176
... constants c1 are uniformly bounded . Similarly , multiplying each of the functions k by a suitable positive constant cn , we may suppose without loss of generality that each of the functions k , has total variation 1 ; here we have used ...
... constants c1 are uniformly bounded . Similarly , multiplying each of the functions k by a suitable positive constant cn , we may suppose without loss of generality that each of the functions k , has total variation 1 ; here we have used ...
Page 1730
... constant A < ∞ such that ( Tf , g ) ≤ Afg | p ) f , ge Co ( C ) . Now we shall prove an important lemma on elliptic partial differential equations with constant coefficients . 18 LEMMA . Let o be a formal partial differential operator ...
... constant A < ∞ such that ( Tf , g ) ≤ Afg | p ) f , ge Co ( C ) . Now we shall prove an important lemma on elliptic partial differential equations with constant coefficients . 18 LEMMA . Let o be a formal partial differential operator ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero