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

On the class SI of J-contractive functions intertwining solutions of linear differential equations

In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class SC of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of SI and elements in SC. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.Comment: 46 page

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

Canonical, squeezed and fermionic coherent states in a right quaternionic Hilbert space with a left multiplication on it

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states, fermionic coherent states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate squeezed states can be defined on the same Hilbert space, but the noncommutativity of quaternions prevents us in getting the desired results.Comment: Conference paper. arXiv admin note: text overlap with arXiv:1704.02946; substantial text overlap with arXiv:1706.0068

Exploring the impact of firm- and relationship-specific factors on alliance performance: Evidence from Turkey

This study investigates the impact of firm-specific (i.e., alliance orientation and partner selection criteria) and relationship-specific (i.e., strategic fit, cultural fit, and organizational fit) factors on alliance performance and assesses the mediating role of trust in the relationship between relationship-specific factors and alliance performance. Partial least squares analysis is applied to a data set of 106 strategic alliances, including both equity alliances (joint ventures) and non-equity alliances (contractual alliances). The empirical results reveal that alliance orientation and strategic fit lead to superior alliance performance and that cultural fit is positively related to partner trustworthiness. The results have managerial implications regarding how to maximize the positive outcomes of an alliance

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

Structural phase transitions in epitaxial perovskite films

Three different film systems have been systematically investigated to understand the effects of strain and substrate constraint on the phase transitions of perovskite films. In SrTiO$_3$ films, the phase transition temperature T$_C$ was determined by monitoring the superlattice peaks associated with rotations of TiO$_6$ octahedra. It is found that T$_C$ depends on both SrTiO$_3$ film thickness and SrRuO$_3$ buffer layer thickness. However, lattice parameter measurements showed no sign of the phase transitions, indicating that the tetragonality of the SrTiO$_3$ unit cells was no longer a good order parameter. This signals a change in the nature of this phase transition, the internal degree of freedom is decoupled from the external degree of freedom. The phase transitions occur even without lattice relaxation through domain formation. In NdNiO$_3$ thin films, it is found that the in-plane lattice parameters were clamped by the substrate, while out-of-plane lattice constant varied to accommodate the volume change across the phase transition. This shows that substrate constraint is an important parameter for epitaxial film systems, and is responsible for the suppression of external structural change in SrTiO$_3$ and NdNiO$_3$ films. However, in SrRuO$_3$ films we observed domain formation at elevated temperature through x-ray reciprocal space mapping. This indicated that internal strain energy within films also played an important role, and may dominate in some film systems. The final strain states within epitaxial films were the result of competition between multiple mechanisms and may not be described by a single parameter.Comment: REVTeX4, 14 figure

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

How do learning orientation and strategy yield innovativeness and superior firm performance?

This paper attempts to shed light on the role of learning orientations of firms and their adoption of Porter’s generic strategies on four dependent variables: Behavioral innovativeness, product innovativeness, technological innovativeness and, ultimately, firm performance. Hierarchical regressions were run with data from a random sample of 121 firms operating in Turkey. Findings indicate that internally-focused learning, market-focused learning and differentiation strategy have significant effects on the three innovativeness dimensions. When firm performance is included as the eventual outcome variable into the analysis, internally-focused learning, focus strategy and product innovativeness emerge as its main predictors. In fast-paced, highly unpredictable market environments, managers can make use of these findings to their benefit in terms of elevating their firms’ innovativeness and performance levels