111 research outputs found
Orthogonal testing families and holomorphic extension from the sphere to the ball
Let denote the open unit ball in , and let . We prove that if is an
analytic function on the sphere that extends
holomorphically in each variable separately and along each complex line through
, then is the trace of a holomorphic function in the ball.Comment: 9 pages, 2 figures. Final version to appear in Math.
On the Ekeland-Hofer symplectic capacities of the real bidisc
In with the standard symplectic structure we consider the
bidisc constructed as the product of two open real discs of
radius . We compute explicit values for the first, second and third
Ekeland-Hofer symplectic capacity of . We discuss some
applications to questions of symplectic rigidity.Comment: v3: Final version, to appear in "Pacific J. Math.", 20 page
An extension theorem for regular functions of two quaternionic variables
For functions of two quaternionic variables that are regular in the sense of
Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves
theorem. Namely, we show that a ball contained in the boundary of a domain is a
propagator of regular extendability across the boundary.Comment: v3: Final version, to appear in "Journal of Mathematical Analysis and
Applications", 10 pages, 1 figur
Holomorphic extension from the sphere to the ball
Real analytic functions on the boundary of the sphere which have separate
holomorphic extension along the complex lines through a boundary point have
holomorphic extension to the ball. This was proved in a previous preprint by an
argument of CR geometry. We give here an elementary proof based on the
expansion in holomorphic and antiholomorphic powers
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