## Analytic Functions of Several Complex Variables |

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Page 248

Incidentally, we could replace the contour C(u) by any other contained in the

intersection of u = const and the shell. The

function throughout the sphere I z ]2 + |u2| < R which is analytic in z for u fixed.

Incidentally, we could replace the contour C(u) by any other contained in the

intersection of u = const and the shell. The

**result**of this first step is to define afunction throughout the sphere I z ]2 + |u2| < R which is analytic in z for u fixed.

Page 294

It is a classical

Hethodcn tier .\IaihemĒ_1tischen Physik II pp. 425-430) that the vanishing of a

solution of the wave equation in a time-like cylinder implies its vanishing in the ...

It is a classical

**result**in the theory of hyperbolic egyations (see Courant-HilbertHethodcn tier .\IaihemĒ_1tischen Physik II pp. 425-430) that the vanishing of a

solution of the wave equation in a time-like cylinder implies its vanishing in the ...

Page 308

Without having heard of these unpublished arguments, L. Garding made a direct

and mathematically rigorous proofofthe

work remained unpublished except in the form of lecture notes : A. S. WIGI-

ITMAN, ...

Without having heard of these unpublished arguments, L. Garding made a direct

and mathematically rigorous proofofthe

**results**of Jost and Lehmann, but thiswork remained unpublished except in the form of lecture notes : A. S. WIGI-

ITMAN, ...

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### Contents

Definition of an Analytic Function Analytic Continuation 229 | 230 |

Holomorphy Domains and Holomorphy Envelopes | 246 |

The Continuity Theorem _ | 259 |

6 other sections not shown

### Common terms and phrases

analogous analytic continuation analytic functions analytic manifold analytic tangent space applications argument Behnke Bremmermann CARTAN compact set complex numbers complex variables connected continuity theorem converge uniformly coordinates defined definition derivatives differential form dimensional dimensions distinguished boundary double cone subtended doubly inadmissible Dyson equivalent example Exercise exists f is holomorphic Figure Fourier transform function analytic function f functions holomorphic germ holomorphic functions holomorphy domain holomorphy envelope homeomorphism hyper-plane infinitely differentiable function intersection Laplace transform limiting disc linear mapping Math maximum natural boundary neighborhood obtained ofthe open set origin polynomial power series proof prove pseudo-convex real axis region representation result Riemann surface satisfies schlicht domain Silov boundary simultaneous continuation singularities solution space-like surface sphere Stokes theorem subdomain subset sufficiently small support of G(p support properties Suppose temperate distribution time-like segment tube uniform convergence upper half plane vacuum expectation value vanishes vector wave equation