23,908 research outputs found
On Some Analytic Functions Defined by a Multiplier Transformation
We introduce and study a new class of analytic functions defined in the unit disc using a certain multiplier transformation.
Some inclusion results and other interesting properties of this class are investigated
Partial orders on partial isometries
This paper studies three natural pre-orders of increasing generality on the
set of all completely non-unitary partial isometries with equal defect indices.
We show that the problem of determining when one partial isometry is less than
another with respect to these pre-orders is equivalent to the existence of a
bounded (or isometric) multiplier between two natural reproducing kernel
Hilbert spaces of analytic functions. For large classes of partial isometries
these spaces can be realized as the well-known model subspaces and
deBranges-Rovnyak spaces. This characterization is applied to investigate
properties of these pre-orders and the equivalence classes they generate.Comment: 30 pages. To appear in Journal of Operator Theor
Inverse Jacobian multipliers and Hopf bifurcation on center manifolds
In this paper we consider a class of higher dimensional differential systems
in which have a two dimensional center manifold at the origin
with a pair of pure imaginary eigenvalues. First we characterize the existence
of either analytic or inverse Jacobian multipliers of the systems
around the origin, which is either a center or a focus on the center manifold.
Later we study the cyclicity of the system at the origin through Hopf
bifurcation by using the vanishing multiplicity of the inverse Jacobian
multiplier.Comment: 22. Journal of Differential Equation, 201
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