The Weiss conjecture and weak norms

In this paper, we study a discrete version of the Weiss Conjecture. In Section 1 we discuss the Reproducing Kernel Thesis and in Section 2 we introduce the operators which concern us. Section 3 shows how to relate these operators to Carleson embeddings and weighted composition operators, so that we can apply the Carleson measure theorem to obtain conditions for boundedness and compactness of many weighted composition operators. Section 4 contains Theorem 4.4 which is a discrete version of the Weiss Conjecture for contraction semigroups, and finally Section 5 shows how the usual (continuous time) Weiss Conjecture is related to the discrete version studied here; in fact they are equivalent (for scalar valued observation operators). The main advantage of the discrete version is that it is technically simpler – the observation operators are automatically bounded and the functional calculus can be achieved using power series.

Some simple representations of the norms in Bergman-Selberg spaces on strips and the right half plane on the complex plane are given. At the same time, analytic extension formulas of functions to the members of the Bergman-Selberg spaces on the strips and the right half plane are established.

Dirichlet series with real frequencies which represent entire functions on the complex plane ℂ have been investigated by many authors. Several properties such as topological structures, linear continuous functionals, and bases have been considered. Le Hai Khoi derived some results with Dirichlet series having negative real frequencies which represent holomorphic functions in a half plane. In the present paper, we have obtained some properties of holomorphic Dirichlet series having positive exponents, whose coefficients belong to a Banach algebra.

An application of GMRES to indefinite linear problems in meteorology

Single-ended primary-inductor converter (SEPIC) based differential inverters (SEPIC-BDI) have received wide concerns in renewable energy applications due to their modularity, galvanic isolation, decreased power stages, continuous input current, and step up/down capability. However, its design still has several challenges related to component design, the existence of complex right half plane (RHP) zeros, and increased sensitivity to component mismatches. In this context, this paper presents an improved control and enhanced design method for the three-phase SEPIC-BDI for grid-tied applications. A generalized static linearization approach (SLA) is proposed to mitigate the low-order harmonics. It practically simplifies the control complexity and decreases the required control loops and sensor circuits. The mismatch between the SEPIC converters in each phase is highly mitigated due to the independent operation of the SLA in each phase and the output dc offset currents are reduced. The proposed enhanced design methodology modifies the SEPIC open-loop transfer function by moving the complex RHP zeros to the left half-plane (LHP). Therefore, a simple proportional-integral (PI) controller effectively maintains converter stability without adding higher-order compensators in the literature. Moreover, a straightforward integrator in the control loop eliminates the negative sequence harmonic component (NSHC) and provides a low computational burden. Simulations and experimental results based on 200V, 1.6 kW, 50 kHz prototype with silicon carbide (SiC) devices are provided to validate the effectiveness of the proposed work. The results show that the proposed controller and design method achieve pure output current waveforms at various operating points of the inverter and dc voltage variations.

We define certain new large area Nevanlinna type spaces in circular ring K on a complex plane and provide complete decriptions of ideals of these new scales of spaces.Our results extend some previously known assertions.

A direct method is porposed for determining eigenvalue distribution of a matrix with respect to several important regions of the complex plane. These regions include half planes, shifted half planes, hyperbolas, sectors, quadrants, imaginary axis, region contined within two straight lines that pass through the orgin etc. The method neither requires computation of the characteristic polynomial of the given matrix nor solution of any matrix equations. The method is illustrated by means of several simple examples.

A new algebraic criterion is given for a polynomial phi with complex coefficients to have all its zeros in a certain type of algebraic region T of the complex plane. In particular, T may be any circle or half plane. The criterion is effectively computable from the coefficients of the polynomial phi. The classical results of Hermite, Hurwitz, Lyapunov, Schur-Cohn, and others appear as special cases of the new criterion.

We prove optimal integrability results for solutions of the $${p(\cdot )}$$ -Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map $$L^1$$ to variable exponent weak Lebesgue spaces.

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

We consider the family of finite signed measures on the complex plane \(\mathbb {C}\) with compact support, of finite logarithmic energy and with zero total mass. We show directly that the logarithmic potential of such a measure sits in the Beppo Levi space, namely, the extended Dirichlet space of the Sobolev space of order 1 over \(\mathbb {C}\), and that the half of its Dirichlet integral equals the logarithmic energy of the measure. We then derive the (local) Markov property of the Gaussian field \(\textbf {G}(\mathbb {C})\) indexed by this family of measures. Exactly analogous considerations will be made for the Beppo Levi space over the upper half plane \(\mathbb {H}\) and the Cameron-Martin space over the real line \(\mathbb {R}\). Some Gaussian fields appearing in recent literatures related to mathematical physics will be interpreted in terms of the present field \(\textbf {G}(\mathbb {C})\).

In this paper, we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz–Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann surface and billiard motions in a regular stellated n-gon in the complex plane.

In this paper, we shall establish sufficient conditions for the uniform ultimate boundedness of solutions of a certain third order nonlinear non-autonomous differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.

In this brief, the distributed state and parameter estimation problem is addressed for a class of discrete-time nonlinear systems subject to sensor saturations over wireless sensor networks. In this regard, a novel estimation design is proposed that involves identification of an unknown parameter under event-triggering mechanism. A sufficient condition for exponential uniform ultimate boundedness of estimation error is established using Lyapunov stability theory. The estimator gains to ensure boundedness of error are linked to the solution of inequality constraints. Finally, the effectiveness of proposed estimator is demonstrated using a simulation example.

Focusing on coordination and consensus, this paper, addresses a control problem for a group of unmanned underwater vehicles (UUVs) by tracking a maneuvering target with varying velocity and time delays. To realize coordinated target tracking, consensus control of multiple UUVs requires neighboring UUV state information, detected target state information, and estimated target acceleration information. At least one UUV is assumed to be capable of obtaining information about the target, and the communication topology graph of the vehicle is assumed to be undirected connected. We consider the convergence analysis of this multi-UUV system for two conditions: information interaction between the target and an UUV with time delays and information interaction between the target and an UUV without time delays. Sufficient conditions for the uniform ultimate boundedness of the tracking errors and estimation errors are obtained by utilizing a Lyapnov-Krasovskii functional. Two simulations are presented to demonstrate the effectiveness of the proposed method.