V C C such that struction of the stalk 61 p z(p) = 0 0 The con- .

Kenning and H. Rossi, Analytic Functions of Several Complex Variables, p. ) The theorem implies that an arbitrary divisor on M is the divisor of a global meromorphic function on M . The Weierstrass factor-theorem gives an explicit representation for a function with the prescribed divisor; (see for instance L. Ahlfors, Complex Analysis, p. 1,57, (McGraw-Hill, 1953) ) For compact Riemann surfaces the preceding theorem does not hold at all; we shall see eventually that (M, A) # 0 . An investigation of the precise extent to which the theorem fails will be one of the main topics of consideration.

Exist a set UP is an isomorphism, P(fa) = 0 , that is, that Then for each point such thatN p E Up C Ua and these sets (Ucover Ua , presheaf that p . p e Ua there must poa(fa) Since it follows from property (i) of a complete Next, consider any section fa = 0 . 0 . f e r(Ua, al ) . For each point p e Ua there must exist a set UP with p e UP C Ua , and an element f13 e 1j such that ppp(fP) = f(p) . P and [fe] coincide at so by restricting UP points p , hence in a full open neighborhood of p ; further if necessary, The seta (UJ) q e Up .

### An Introduction to Laplace Transforms and Fourier Series (2nd Edition) (Springer Undergraduate Mathematics Series) by Phil Dyke

by Michael

4.2