Markov Chains, Riesz Transforms and Lipschitz Maps.
Markov-Krein transform
The Markov-Krein transform maps a positive measure on the real line to a probability measure. It is implicitly defined through an identity linking two holomorphic functions. In this paper an explicit formula is given. Its proof is obtained by considering boundary values of holomorhic functions. This transform appears in several classical questions in analysis and probability theory: Markov moment problem, Dirichlet distributions and processes, orbital measures. An asymptotic property for this transform...
Matematika dokonale ukrytá v počítačové tomografii
Matrix computation and the theory of moments.
Matrix-Variate Statistical Distributions and Fractional Calculus
MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...
Maximal functions and Hilbert transforms associated to polynomials.
Maximum d'entropie et problème des moments
Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the...
Mean-periodic operational calculi
Elements of operational calculi for mean-periodic functions with respect to a given linear functional in the space of continuous functions are developed. Application for explicit determining of such solutions of linear ordinary differential equations with constant coefficients is given.
Möbius convolutions and the Riemann hypothesis.
Modified dyadic derivatives and integrals of fractional order on .
Modulating element method in the identification of a generalized dynamical system
In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.
Modulation invariant and multilinear singular integral operators
In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...
Moment problem and its application [Abstract of thesis]
Moment problems and polynomial approximation
Moment sequences and abstract Cauchy problems
We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.
Moments of vector measures and Pettis integrable functions
Conditions, under which the elements of a locally convex vector space are the moments of a regular vector-valued measure and of a Pettis integrable function, both with values in a locally convex vector space, are investigated.
More on the Weeks Method for the Numerical Inversion of the Laplace Transform.
Motion planning for a class of boundary controlled linear hyperbolic PDE’s involving finite distributed delays
Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński’s...
Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays
Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing ...