Let H∞(B) be the Banach algebra of bounded holomorphic functions on the open unit ball B of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on H∞(B). This answers ...
We give an alternative description of the Carathéodory pseudodistance on a domain D in an arbitrary complex Banach space. This gives a Schwarz lemma for holomorphic maps of the domain.We specialise to the case of a bounded ...
We show that the scaling spaces de ned by the polysplines of order
p provide approximation order 2p: For that purpose we re ne the re-
sults on one dimensional approximation order by L-splines obtained
in [2].
Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given. In addition, ...
Our main result states that two signed measures μ and ν with bounded
support contained in the zero set of a polynomial P(χ) are equal if they coincide on the
subspace of all polynomials of polyharmonic degree NP where ...
Let
p,n
∈
N
with 2
p
≥
n
+ 2
,
and let
I
a
be a polyharmonic spline of
order
p
on the grid
Z
×
a
Z
n
which satisfies the interpolating conditions
I
a
(
j,am
) =
d
j
(
am
) for
j
∈
Z
,m ...
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+1) be the space of all C∞-solutions of
LN+1 on the real line.We show that for N 2 and ...
In [O'S], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras defined over local fields. In this paper, the level and sublevel of composition algebras, of ...
In this paper a positive answer is given to the following question of W.K.
Hayman: if a polyharmonic entire function of order k vanishes on k distinct ellipsoids
in the euclidean space Rn then it vanishes everywhere. ...
We consider a problem of mixed Cauchy type for certain holomorphic partial differential
operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to
a power, Δp. We provide inital data on ...
We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. ...
The reproducing kernel of the space of all homogeneous polynomi-
als of degree
k
and polyharmonic order
m
is computed explicitly, solving a
question of A. Fryant and M.K. Vemuri.
Methods of Padè approximation are used to analyse a multivariate
Markov transform which has been recently introduced by the authors.
The first main result is a characterization of the rationality of the
Markov transform ...
An observational study was carried out, using data collected from four areas in the Irish midlands, between 1989 and 2004, to critically evaluate the long-term effects of proactive badger culling and to provide insights ...
In this note, we look at homotopes of Jordan triple structures and show that, following a renorming, an isotope of a JB*-triple is also a JB*-triple. We also provide a proof of the Russo—Dye theorem for JBW*-triples.
Let
L
be a linear differential operator with constant coefficients of order
n
and complex eigenvalues
λ
0
,...,λ
n
. Assume that the set
U
n
of all solutions of the
equation
Lf
= 0 is closed under complex ...
The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The
analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion ...
We study the dynamics of a spherical rigid body that rocks and rolls on a plane
under the effect of gravity. The distribution of mass is non-uniform and the
centre of mass does not coincide with the geometric centre. The ...