Linear Operators: General theory |
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Page 3
... domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for x in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by ƒ | A . If ƒ : A → B , and for each be f ( A ) there is only ...
... domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for x in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by ƒ | A . If ƒ : A → B , and for each be f ( A ) there is only ...
Page 230
... domain U in Z is connected if and only if every pair of its points lies on some simple Jordan curve contained in U. 1 Let f be a function analytic on a domain U in the space of n complex variables , and let g be an analytic function ...
... domain U in Z is connected if and only if every pair of its points lies on some simple Jordan curve contained in U. 1 Let f be a function analytic on a domain U in the space of n complex variables , and let g be an analytic function ...
Page 605
... domain D ( T ) { xx is absolutely continuous and x ' e L ( -л , л ) } . Show that T is a closed unbounded operator whose domain is dense for p < ∞∞ , whose spectrum is the set { in } , n = 0 , 1 , 2 , ... , and that σ ( T ) = σ , ( T ) ...
... domain D ( T ) { xx is absolutely continuous and x ' e L ( -л , л ) } . Show that T is a closed unbounded operator whose domain is dense for p < ∞∞ , whose spectrum is the set { in } , n = 0 , 1 , 2 , ... , and that σ ( T ) = σ , ( T ) ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ