Difference properties of higher orders for continuity and Riemann integrability
Differentiable solutions for a class of functional equations
We give a set of sufficient conditions for the existence of differentiable solutions for a functional equation involving a series of iterates, using a method different from that of Baker and Zhang [Ann. Polon. Math. 73 (2000)].
Differentiable solutions of equations involving iterated functional series.
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices
2000 Mathematics Subject Classification: 42C05.We give an easy procedure for solving of the direct and the inverse spectral problems for the equation. Guseynov used a procedure of the Gelfand-Levitan type for the case N = 1. We use another procedure and this procedure is more easy and transparent.
Directionally convex ordering in multidimensional jump diffusions models.
Dirichlet boundary value problems of nonlinear functional difference equations with Jacobi operators.
Discrete analogues of singular and maximal Radon transforms.
Discrete Analogues of the Heisenberg-Weyl Algebra.
Discrete analogues of Wirtinger's inequality for a two-dimensional array
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 differential operators in multidimensional Haar wavelet spaces.
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 fractional calculus with the nabla operator.
Discrete inequalities of Wirtinger's type for higher differences.
Discrete isothermic surfaces.
Discrete singular functionals
In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.
Discrete spectra criteria for singular difference operators
We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).
Discretely normed Abelian groups.
Discretized representations of harmonic variables by bilateral Jacobi operators.