Dirichlet series associated with polynomials
Dirichlet series with functional equations and related arithmetical identities
Dirichlet's Principle, Uniqueness of Harmonic Maps and Extremal QC Mappings
Dirichletsche Reihen auf arithmetischen Progressionen.
Disconnected Julia set and rotation sets
Discrete complex analysis – the medial graph approach
We discuss a new formulation of the linear theory of discrete complex analysis on planar quad-graphs based on their medial graphs. It generalizes the theory on rhombic quad-graphs developed by Duffin, Mercat, Kenyon, Chelkak and Smirnov and follows the approach on general quad-graphs proposed by Mercat. We provide discrete counterparts of the most fundamental objects in complex analysis such as holomorphic functions, differential forms, derivatives, and the Laplacian. Also, we discuss discrete versions...
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete groups and thin sets.
Disjoint hypercyclic operators
We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.
Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall.
Diskrete Deformation Fuchsscher Gruppen und ihrer automorphen Formen.
Disques de Siegel et anneaux de Herman
Disques extrémaux et surfaces modulaire
Distance between domains in the sense of Letho is not a metric.
Distance entre les racines d'un polynôme
Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann -function
It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann -function.
Distances from Bloch functions to some Möbius invariant spaces.
Distortion function and quasisymmetric mappings
We study the relationship between the distortion function and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.
Distortion of the exponent of convergence in space.
Distortion theorems for fractional calculus of certain analytic functions with negative coefficients.