CR-continuation of arc-analytic maps

5 Extremal Discs and Analytic Continuation of Product Cr Maps

On the Convergence of S-nondegenerate Formal Cr Maps between Real Analytic Cr Manifolds

A new pointwise nondegeneracy condition about generic real analytic submanifolds in Cn, called S-nondegeneracy, is introduced. This condition is intermediate between essential finiteness and holomorphic nondegeneracy. We prove in this paper that a formal biholomorphism between S-nondegenerate and minimal real analytic CR generic manifolds is convergent, generalizing by this earlier results of C...

On Effective Analytic Continuation

Until now, the area of symbolic computation has mainly focused on the manipulation of algebraic expressions. It would be interesting to apply a similar spirit of “exact computations” to the field of mathematical analysis. One important step for such a project is the ability to compute with computable complex numbers and computable analytic functions. Such computations include effective analytic...

Analytic continuation of multiple polylogarithms

It is not hard to see that this function can be analytically continued to a multi-valued memomorhpic function on C. When n > 1 the special value Lin(1) is nothing else but the Riemann zeta value ζ(n), which has great importance in number theory. In recent years, there has been revival of interest in multi-valued classical polylogarithms and their single-valued cousins. For any positive integers...

Analytic Continuation of the Resolvent

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work [9] we described the resolvent, and specifically the asymptotic behavior of the Green’s function, on SL(3)/ SO(3) using methods from three-particle scattering....