A new theory for the rational covariance extension problem (with degree constraint), or simply the RCEP, has recently emerged with applications in high-resolution spectral estimation, speech synthesis and possibly new applications in time series analysis and system identification. This paper establishes some new theoretical results on the RCEP via an alternative analysis. In one result we show ...

This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation-minimization by a unit element. Next, by the modifi...

We proved that the Hurwitz zeta function is prime. In addition, we derived Nevanlinna characteristic for this function.

By using the second main theorem of the meromorphic function on annuli, we investigate the problem on two meromorphic functions partially sharing five or more values and obtain some theorems that improve and generalize the previous results given by Cao and Yi.

In this article, a meromorphic function means meromorphic in the open complex plane. We assume that the reader is familiar with the Nevanlinna theory of meromorphic functions and the standard notations such as T r, f , m r, f , N r, f ,N r, f , and so on. Let f and g be two nonconstant meromorphic functions; a meromorphic function a z /≡∞ is called a small functions with respect to f provided t...

In this paper we will consider the Nevanlinna-Pick problem for a class of subalgebras of H∞. Let us assume that we are given n points z1, . . . , zn ∈ D, n complex numbers w1, . . . , wn and a subalgebra A of H ∞. We will say that a function f ∈ A, interpolates the values z1, . . . , zn to w1, . . . , wn if and only if ‖f‖∞ ≤ 1 and f(zj) = wj . Such an f will be called an interpolating function...

We consider the stabilization of networked control systems with time-invariant clock offset between the sensors and the controllers. Clock offsets are modeled as parametric uncertainty and we provide necessary and sufficient conditions for the existence of a single controller that is capable of stabilizing the closed loop for every parameter value in a given range. For scalar systems, using the...

This paper examines the connections between feedback stabilization and H∞ control, model matching problems and multivariable Nevanlinna-Pick interpolation problems for multidimensional or nD linear systems.

Using potential theoretic methods we give extension results for functions in various Hardy classes and in the Nevanlinna class in C". Our exceptional sets are polar or slightly larger n-small sets depending whether the majorant is a harmonic or separately hyperharmonic function.