Analytic Functions of Several Complex Variables |
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Page 308
... upper half plane . The analytic function f ( z ) then has a continuous boundary value f ( x ) , which is the Fourier transform of g ( k ) . We take these statements as known . ( The analyticity is intuitively obvious since the factor e ...
... upper half plane . The analytic function f ( z ) then has a continuous boundary value f ( x ) , which is the Fourier transform of g ( k ) . We take these statements as known . ( The analyticity is intuitively obvious since the factor e ...
Page 309
... upper half plane , for example , that the limit lim √ q ( x ) F ( x + iy ) dx = f ( q ) exists for every infinitely differentiable function of compact support , and f ( ) defines a distribution . Bear in mind that as an analytic ...
... upper half plane , for example , that the limit lim √ q ( x ) F ( x + iy ) dx = f ( q ) exists for every infinitely differentiable function of compact support , and f ( ) defines a distribution . Bear in mind that as an analytic ...
Page 310
... upper half plane even though cosh Vk √k increases at k = + faster than any power of k and therefore is not temperate . This shows that further conditions on f ( z ) will be necessary to insure that g ( k ) is a temperate distribution ...
... upper half plane even though cosh Vk √k increases at k = + faster than any power of k and therefore is not temperate . This shows that further conditions on f ( z ) will be necessary to insure that g ( k ) is a temperate distribution ...
Contents
Introduction | 228 |
The JostLehmannDyson Representation | 291 |
Laplace Transforms Analytic Functions and Temperate | 308 |
1 other sections not shown
Common terms and phrases
analytic continuation analytic functions analytic manifold analytic tangent space Behnke Bochner CARTAN class of functions complex variables connected continuity theorem converges uniformly convex defined Definition derivatives dimensional dimensions distinguished boundary doubly inadmissible Dyson dz₂ example Exercise exists f is holomorphic f(z₁ face Figure formula Fourier transform function analytic function f functions holomorphic Funktionen mehrerer Gårding holomorphic functions holomorphy domain holomorphy envelope homeomorphism hyper-plane hypersurface intersection Laplace transform limiting disc local homeomorphism mapping Math neighborhood obtained open set polycircle polynomial power series proof prove pseudo-convex real axis region Riemann surface satisfies Šilov boundary singularities solution space-like surface Stokes theorem subdomain subset sufficiently small support of G(p support properties Suppose temperate distribution theory tube uniform convergence upper half plane vacuum expectation value vanishes w₁ wave equation z₁ z₂ zero