Their topics include the Cauchy-Kovalevskaya theorem with estimates, applications of the Bony-Schapira theorem: Vekua Hulls and Szego's theorem revisited, potential theory on ellipsoids, singularities encountered by the
analytic continuation of solutions to the Dirichlet problem, and quadrature domains and Laplacian growth.
Several authors have studied the
analytic continuation of the multiple zeta function and proved that the multiple zeta function [zeta]([s.sub.1], ...,[s.sub.d]) of depth d can be analytically continued to a meromorphic function on all of [C.sup.d].
Application of principle of
analytic continuation to (15) implies
analytic continuation of the functions [[phi].sup.(0).sub.k] and [[phi].sup.(0).sub.0] (z) into all the domains [D.sub.k].
Zheng, "Multiplication operators on the Bergman space via
analytic continuation," Advances in Mathematics, vol.
Under the condition (2.8), the Jost solution E(*,z) has an
analytic continuation from [D.sub.0] to {z [member of] C : [absolute value of (z)] < 1} \{0}.
Indeed, the inverse function may have an
analytic continuation to A, with
We now consider the function E(s) as the
analytic continuation of Euler numbers.
By q-Euler zeta function, we consider the function [E.sub.q](s) as the
analytic continuation of q-Euler numbers.
Analytic Continuation of (h, q)-Euler Numbers [E.sup.(h).sub.n,q]
where the function g is the
analytic continuation of [f.sup.-1](w) to U.
of Oxford) introduces the constructive approximation of polynomials and rational functions, and extends the techniques to interpolation, quadrature, rootfinding,
analytic continuation, extrapolation of sequence and series, and solution of differential equations.
The transfer rules also apply when there are finitely many singularities [[zeta].sub.1], ..., [[zeta].sub.l] on the boundary of the disk of convergence, provided
analytic continuation holds in a [DELTA]-domain of the form [[zeta].sub.i] x [OMEGA] around each singularity.