Let α ∈ C in the upper half-plane and let I be an interval. We construct an analogue of Selberg’s majorant of the characteristic function of I that vanishes at the point α. The construction is based on the solution to an extremal problem with positivity and interpolation constraints. Moreover, the passage from the auxiliary extremal problem to the construction of Selberg’s function with vanishi...

In this paper the problem of practical stabilization for a significant class of MIMO uncertain pseudo-linear and pseudoquadratic systems, with additional bounded nonlinearities and/or bounded disturbances, is considered. By using the concept of majorant system, via Lyapunov approach, new fundamental theorems, from which derive explicit formulas to design state feedback control laws, with a poss...

Let f(z) akzk a 0 be analytlc in the unlt disc. Any k=O o Inflnlte complex vector e (eo,et,e2 ) such that lekl 1, k 0,1,2 induces a function re(Z) akekZk whlch is still analytic k=O In the unit disc. In this paper we study the problem of maximizing the p-means: over all possible vectors e and for values of r close to 0 and for all p<2. k It is proved that a maxlmlzlng function Is f,{z} -laoi + ...

We establish the existence of solutions to Cauchy problem for a large class nonlinear parabolic equations including fractional semilinear equations, higher-order and viscous Hamilton–Jacobi by using majorant kernel introduced in Ishige et al. (2020).

We give exact estimations of certain weighted L-norms of the k-th derivative of polynomials which have a curved majorant. They are all obtained as applications of special quadrature formulae.

We construct a continuous distribution G such that the number of faces in the smallest concave majorant of the random walk with G-distributed summands will take on each natural number infinitely often with probability one. This investigation is motivated by the fact that the number of faces Fn of the concave majorant of the random walk at time n has the same distribution as the number of record...

We consider a convex variational problem related to a time-step problem in elasto-plastic models with isotropic hardening. Our goal it to derive a posteriori error estimate of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. The estimates are obtained by a advanced version of the variational approach earlier used for linear b...

We consider a Poisson problem and its functional a posteriori estimate derived in [20]. The estimate majorizes the L2 norm of the error of the discrete solution computed by FEM method and contains a free variable from a H(div) space. In order to keep the estimate sharp, the majorant term is minimized with respect to the free variable. A minimization procedure is introduced, containing a solutio...