Linear Operators, Part 2 |
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Page 1434
... infinity . Suppose that we are dealing with an equation of the form [ ** ] - n Σ αx ( z ) z v ( n − k ) f ( k ) ( z ) ... infinity ; if v > −1 , [ ** ] is said to have an irregular singularity of order v + 2 at infinity . If [ ** ] has a ...
... infinity . Suppose that we are dealing with an equation of the form [ ** ] - n Σ αx ( z ) z v ( n − k ) f ( k ) ( z ) ... infinity ; if v > −1 , [ ** ] is said to have an irregular singularity of order v + 2 at infinity . If [ ** ] has a ...
Page 1528
... infinity with characteristic sets [ ( 1 ) +5 ( 1 ) , . . . , 5 ( x - 1 ) + ¿ ( k − 1 ) , e ; + e ] , i = 1 , 2. If z ( w ) is a rational function of w of the form с aw 1 + 70 + d + W2 · · 9 s≥ 1 , = in the neighborhood of infinity ...
... infinity with characteristic sets [ ( 1 ) +5 ( 1 ) , . . . , 5 ( x - 1 ) + ¿ ( k − 1 ) , e ; + e ] , i = 1 , 2. If z ( w ) is a rational function of w of the form с aw 1 + 70 + d + W2 · · 9 s≥ 1 , = in the neighborhood of infinity ...
Page 1557
... infinity , and hence so does ( f ) ' , and thus also f2 , contradiction . Ad ( d ) : derive the intermediary ... infinity . = G22 Let q ( t ) -12 log4 t . Prove that the operator 7 has two boundary values at infinity . G23 ( Hartman ) ...
... infinity , and hence so does ( f ) ' , and thus also f2 , contradiction . Ad ( d ) : derive the intermediary ... infinity . = G22 Let q ( t ) -12 log4 t . Prove that the operator 7 has two boundary values at infinity . G23 ( Hartman ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero