Linear Operators, Part 1 |
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Page 224
Functions of a Complex Variable In some of the chapters to follow, and especially
in Chapter VII, we shall use extensions of certain well-known results in the theory
of analytic functions of a complex variable to the case where the functions are ...
Functions of a Complex Variable In some of the chapters to follow, and especially
in Chapter VII, we shall use extensions of certain well-known results in the theory
of analytic functions of a complex variable to the case where the functions are ...
Page 230
If no a, with p < 0 is non-zero, and if we put f(zo) = an; then f becomes analytic in
2–zo & r, so that the singularity at z = zo is removable. If a, - 0 for p < 0, z0 is
called a zero of f; thus zo is a zero of f if f(zo) = 0. If, in this case, a, - 0 for p < n but
a, ...
If no a, with p < 0 is non-zero, and if we put f(zo) = an; then f becomes analytic in
2–zo & r, so that the singularity at z = zo is removable. If a, - 0 for p < 0, z0 is
called a zero of f; thus zo is a zero of f if f(zo) = 0. If, in this case, a, - 0 for p < n but
a, ...
Page 586
o Then there evists a 6 - 0 such that if u → 6, then U Co(T(u)) and R(A; T(u)) is an
analytic function of u for each A. e U. PRoof. By Lemma 3, there is a 6, such that if
u → 31, then U Co(T(u)). Let 0 < 0, be chosen such that T(0)—T(u) < inf R(A; ...
o Then there evists a 6 - 0 such that if u → 6, then U Co(T(u)) and R(A; T(u)) is an
analytic function of u for each A. e U. PRoof. By Lemma 3, there is a 6, such that if
u → 31, then U Co(T(u)). Let 0 < 0, be chosen such that T(0)—T(u) < inf R(A; ...
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Contents
A Settheoretic Preliminaries | 1 |
Convergence and Uniform Convergence of Generalized | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
27 other sections not shown
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Common terms and phrases
additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz 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 zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Nelson Dunford Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |