Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 54
Page 1629
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
Page 1639
... partial differential operator of the form T = Σ αγ ( π ) , Jsm then the formal partial differential operator T * = Σ ( −1 ) αл ( x ) J≤m is called the adjoint , or formal adjoint of τ . If r = 7 * , then 7 is said to be formally ...
... partial differential operator of the form T = Σ αγ ( π ) , Jsm then the formal partial differential operator T * = Σ ( −1 ) αл ( x ) J≤m is called the adjoint , or formal adjoint of τ . If r = 7 * , then 7 is said to be formally ...
Page 1705
... partial differential operator of order at most p - 1 . It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( foS ) = fe , that the distribution fep satisfies the partial differential equation ( 2 ) Σ aj ( εx ) ...
... partial differential operator of order at most p - 1 . It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( foS ) = fe , that the distribution fep satisfies the partial differential equation ( 2 ) Σ aj ( εx ) ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
Common terms and phrases
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 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 PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero