988 research outputs found
On the mixed Cauchy problem with data on singular conics
We consider a problem of mixed Cauchy type for certain holomorphic partial
differential operators whose principal part essentially is the
(complex) Laplace operator to a power, . We pose inital data on a
singular conic divisor given by P=0, where is a homogeneous polynomial of
degree . We show that this problem is uniquely solvable if the polynomial
is elliptic, in a certain sense, with respect to the principal part
Polyharmonic functions of infinite order on annular regions
Polyharmonic functions f of infinite order and type {\tau} on annular regions
are systematically studied. The first main result states that the
Fourier-Laplace coefficients f_{k,l}(r) of a polyharmonic function f of
infinite order and type 0 can be extended to analytic functions on the complex
plane cut along the negative semiaxis. The second main result gives a
constructive procedure via Fourier-Laplace series for the analytic extension of
a polyharmonic function on annular region A(r_{0},r_{1}) of infinite order and
type less than 1/2r_{1} to the kernel of the harmonicity hull of the annular
region. The methods of proof depend on an extensive investigation of Taylor
series with respect to linear differential operators with constant
coefficients.Comment: 32 page
Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas
In the present paper we introduce a new concept of Hardy type space naturally
defined on the Klein-Dirac quadric. We study different properties of the
functions belonging to these spaces, in particular boundary value problems. We
apply these new spaces to polyharmonic interpolation and to interpolatory
cubature formulas.Comment: 32 page
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