Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Contribution of space charges to the polarization of ferroelectric superlattices and its effect on dielectric properties

A theoretical model is developed for ferroelectric bilayers and multilayer heterostructures that employs a nonlinear Landau-Devonshire formalism coupled with a detailed analysis of the depolarizing fields arising from the polarization mismatch across interlayer interfaces and the electrical fields of localized space charges at such interfaces. We first present how space charges alter the free-energy curves of ferroelectrics and then proceed with a numerical analysis for heteroepitaxial (001) PbTiO3-SrTiO3 (PTO-STO) bilayers and (001) superlattice structures on (001) STO substrates. The switchable (ferroelectric) and nonswitchable (built-in) polarizations and the dielectric properties of PTO-STO bilayers and superlattices are calculated as a function of the planar space-charge density and the volume fraction of the PTO layer. Similar to the temperature dependence of a monolithic ferroelectric, there exists a critical volume fraction PTO below which the bilayer or the superlattice is in the paraelectric state. This critical volume fraction is strongly dependent on the density of trapped charges at the interlayer interfaces. For charge-free (001) PTO-STO heteroepitaxial bilayer and superlattices, the critical fraction is 0.40 for both constructs but increases to 0.6 and 0.72, for the bilayer and the superlattice, respectively, for a planar space-charge density of 0.05 C/m(2). Furthermore, our results show that close to the vicinity of ferroelectric-paraelectric phase transition, there is a recovery in ferroelectric polarization. The dielectric-response calculations verify that there is sharp ferroelectric phase transformation for charge-free bilayers and superlattices whereas it is progressively smeared out with an increase in the charge density. Furthermore, our analysis shows that the dielectric constant of these multilayers at a given volume fraction of PTO decreases significantly in the presence of space charges

Wiener algebra for the quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators

Krein systems

In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role

Layer thickness and period as design parameters to tailor pyroelectric properties in ferroelectric superlattices

We theoretically examine the pyroelectric properties of ferroelectric-paraelectric superlattices as a function of layer thickness and configuration using non-linear thermodynamics coupled with electrostatic and electromechanical interactions between layers. We specifically study PbZr0.3Ti0.7O3/SrTiO3 superlattices. The pyroelectric properties of such constructs consisting of relatively thin repeating units are shown to exceed the pyroelectric response of monolithic PbZr0.3Ti0.7O3 films. This is related to periodic internal electric fields generated due to the polarization mismatch between layers that allows tailoring of the shift in the transition temperature. Our results indicate that higher and electric field sensitive pyroresponse can be achieved from layer-by-layer engineered ferroelectric heterostructures

Strong dependence of dielectric properties on electrical boundary conditions and interfaces in ferroelectric superlattices

A computational study based on Landau-Ginzburg-Devonshire theory is carried out to understand the role of interfaces on the dielectric response of ferroelectric superlattices. Using heteroepitaxial (001) PbZr0.3Ti0.7O3/(001)SrTiO3 heterostructures on (001)SrTiO3 as an example, we show that electrostatic boundary conditions have a pronounced effect on the dielectric response far below the ferroelectric phase transition temperature. For a fixed total multilayer thickness, the average dielectric response can be improved significantly for superlattices with a small layer periodicity. This is due to the large total internal electric fields at the interlayer interfaces which originate from the polarization mismatch between layers

Tailoring dielectric properties of ferroelectric-dielectric multilayers

We develop a nonlinear thermodynamic model for multilayer ferroelectric heterostructures that takes into account electrostatic and electromechanical interactions between layers. We concentrate on the effect of relative layer fractions and in-plane thermal stresses on dielectric properties of Ba0.6Sr0.4TiO3-, BaTiO3-, and PbZr0.2Ti0.8O3 (PZT)-SrTiO3 (STO) multilayers on Si and c-sapphire. We show that dielectric properties of such multilayers can be significantly enhanced by tailoring the growth/processing temperature and the STO layer fraction. Our computations show that large tunabilities (similar to 90% at 400 kV/cm) are possible in carefully designed barium strontium titanate-STO and PZT-STO even on Si for which there exist substantially large in-plane strains