R. Narasimhan. Several Complex Variables, University of Chicago Press, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....equation is diagonal, of the form: 8 : h 1 ) t Gamma 1 (h 1 ; h 2 ) h 1 ) z = 0 (h 2 ) t Gamma 2 (h 1 ; h 2 ) h 2 ) z = 0 h 1 (z; 0) h 2 (z; 0) given. 10) Proof: The fact that H has a local holomorphic inverse can be proven using a version of the inverse mapping theorem, see [18]) just by observing that its derivative at Z 0 is an invertible linear transformation. To obtain the diagonalization, start with a solution U(z; t) of equation (9) We can again find Q, an open rectangle containing I, and T positive, and choose data sufficiently close to a constant Z 0 that the ....

R. Narasimhan, Several Complex Variables, University of Chicago Press, Chicago, 1971.

....2 G c , the sequence k de ned inductively by k = L( k 1 ) is in G c . Since the functions in G c are uniformly bounded, k ) itself is uniformly bounded. Furthermore, by the preceding subsection, the sequence is convergent over the reals. Hence, applying Vitali s Theorem (see, for instance, [18]) to each component of k , we have that ( k ) is convergent over compacts sets in the complex domain. Clearly, the limit function is a xed point of L and therefore its graph gives the unstable manifold. Moreover, considering as a complex parameter the uniform estimates with respect to give ....

R. Narasimhan, Several complex variables, Chicago Lectures in Math. Series, University of Chicago Press, 1971.

....to zero or has at most countably many zeros. There is a simple way to obtain a large number of sparse signatures over the reals, using the fact that any analytic function is either identical to zero or has at most countably many zeros, and composition of analytic functions is analytic again [27]. Proposition 2. Let (H 1 ; H 2 ; be any collection of analytic functions such that the value of each H i is in R if all its arguments are in R. Let h i be the restriction of H i to the real arguments. If one of the H i s is subtraction, then Omega = h 1 ; h 2 ; is sparse. 2 Some ....

R. Narasimhan. Several Complex Variables, University of Chicago Press, 1971.

....be realized as the automorphism groups of bounded domains in complex space [SZ] BD] TS] but in this paper we deal only with domains for which Aut(D) is large enough . More precisely, we consider the class of domains for which Aut(D) is non compact. By a classical theorem of H. Cartan (see [N]) for a bounded domain this condition is equivalent to the non compactness of every orbit of the action of Aut(D) on D (which is in fact equivalent to the existence of only one non compact orbit) For example, any homogeneous domain (i.e. domain on which Aut(D) acts transitively) has non compact ....

Narasimhan, R., Several Complex Variables, University of Chicago Press, Chicago, 1971.

....to zero or has at most countably many zeros. There is a simple way to obtain a large number of sparse signatures over the reals, using the fact that any analytic function is either identical to zero or has at most countably many zeros, and composition of analytic functions is analytic again [24]. Proposition 2 Let (H 1 ; H 2 ; be any collection of analytic functions such that the value of each H i is in R if all its arguments are in R. Let h i be the restriction of H i to the real arguments. If one of the H i s is subtraction, then Omega = h 1 ; h 2 ; is sparse. 2 Some ....

R. Narasimhan. Several Complex Variables, University of Chicago Press, 1971.

....sequence fl k defined inductively by fl k = L(fl k Gamma1 ) is in G c . Since the functions in G c are uniformly bounded, fl k ) itself is uniformly bounded. Furthermore, by the preceding subsection, the sequence is convergent over the reals. Hence, applying Vitali s Theorem (see, for instance, [17]) to each component of fl k , we have that (fl k ) is convergent over compacts sets in the complex domain. Clearly, the limit function is a fixed point of L and therefore its graph gives the unstable manifold. Moreover, considering as a complex parameter the uniform estimates with respect to ....

R. Narasimhan, Several complex variables, Chicago Lectures in Math. Series, University of Chicago Press, 1971.

....to zero or has at most countably many zeros. There is a simple way to obtain a large number of sparse signatures over the reals, using the fact that any analytic function is either identical to zero or has at most countably many zeros, and composition of analytic functions is analytic again [26]. Proposition 2 Let (H 1 ; H 2 ; be any collection of analytic functions such that the value of each H i is in R if all its arguments are in R. Let h i be the restriction of H i to the real arguments. If one of the H i s is subtraction, then Omega = h 1 ; h 2 ; is sparse. 2 Some ....

R. Narasimhan. Several Complex Variables, University of Chicago Press, 1971.

....spaces (see Definitions 3.1 and 4.1) As pointed out in [4] those purely algebraic results appear to be very useful in the following complex analytic setting. Let D ae C n be a bounded domain and Aut(D) the group of all holomorphic automorphisms of D . By a theorem of H. Cartan ( 1] see also [8]) Aut(D) is a real Lie group. In [10] Webster gave the conditions on D , such that all automorphisms extend to the birational transformations of the ambient C n . Moreover, as shown in [13] the group Aut(D) has finitely many components in this case. Such properties are also valid for the ....

R. Narasimhan, "Several complex variables", Chicago Lectures in Mathematics. Univ. of Chicago Press, 1971.

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R. Narasimhan. Several Complex Variables, University of Chicago Press, 1971.

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R. Narasimhan, Several complex variables, the University of Chicago press,Chicago and London, (1971).

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