Linear Operators: Spectral theory |
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Page 1217
... called the measure of the ordered representation . The sets e , will be called the multiplicity sets of the ordered representation . If u ( ex ) > 0 and μ ( ex + 1 ) = 0 then the ordered representation is said to have multiplicity k ...
... called the measure of the ordered representation . The sets e , will be called the multiplicity sets of the ordered representation . If u ( ex ) > 0 and μ ( ex + 1 ) = 0 then the ordered representation is said to have multiplicity k ...
Page 1297
... called a boundary value at a . The concept of a boundary value at b is defined similarly . By analogy with Definition XII.4.25 an equation B ( f ) = 0 , where B is a boundary value for T , is called a boundary condition for T. A set of ...
... called a boundary value at a . The concept of a boundary value at b is defined similarly . By analogy with Definition XII.4.25 an equation B ( f ) = 0 , where B is a boundary value for T , is called a boundary condition for T. A set of ...
Page 1432
... called the order of the singularity of equation [ * ] at zero . If v = 0 , there is no singularity at all , and zero is called a regular point of the differential equation . If v = 1 , the singularity of equation [ * ] at zero is called ...
... called the order of the singularity of equation [ * ] at zero . If v = 0 , there is no singularity at all , and zero is called a regular point of the differential equation . If v = 1 , the singularity of equation [ * ] at zero is called ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero