Linear Operators: Spectral theory |
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Page 1175
... mapping of the space Lo ( L ( S ) ) into itself . defined by the formula ξο be the mapping in L. ( L , ( S ) ) ( 47 ) ( H & † ) ( E ) = Î ( E ) , § > 50 , = 0 otherwise . By Corollary 22 , it follows that there is a finite constant C ...
... mapping of the space Lo ( L ( S ) ) into itself . defined by the formula ξο be the mapping in L. ( L , ( S ) ) ( 47 ) ( H & † ) ( E ) = Î ( E ) , § > 50 , = 0 otherwise . By Corollary 22 , it follows that there is a finite constant C ...
Page 1669
... mapping → o M is a continuous mapping of C °° ( 12 ) into C∞ ( I1 ) . ( See Section 2 for a definition of the topology in these spaces . ) By ( a ) , q → M maps Co ( I2 ) into Co ( I1 ) . By ( a ) again , all the functions of the ...
... mapping → o M is a continuous mapping of C °° ( 12 ) into C∞ ( I1 ) . ( See Section 2 for a definition of the topology in these spaces . ) By ( a ) , q → M maps Co ( I2 ) into Co ( I1 ) . By ( a ) again , all the functions of the ...
Page 1707
... mapping of Hm + P ) ( C ) into H ( m ) ( C ) , and of Hm + -1 ) ( C ) into Hm - 1 ) ( C ) , is less than min ( îm , îm − 1 ) . Then , by Lemma VII.3.4 , the mapping ( 1 + 0εtī1 ) , π regarded either as a mapping of H ( m ) ( C ) or of ...
... mapping of Hm + P ) ( C ) into H ( m ) ( C ) , and of Hm + -1 ) ( C ) into Hm - 1 ) ( C ) , is less than min ( îm , îm − 1 ) . Then , by Lemma VII.3.4 , the mapping ( 1 + 0εtī1 ) , π regarded either as a mapping of H ( m ) ( C ) or of ...
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BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero