Localization and Toeplitz Operators on Polyanalytic Fock Spaces

The well know conjecture of {\it Coburn} [{\it L.A. Coburn, {On the Berezin-Toeplitz calculus}, Proc. Amer. Math. Soc. 129 (2001) 3331-3338.}] proved by {\it Lo} [{\it M-L. Lo, {The Bargmann Transform and Windowed Fourier Transform}, Integr. equ. oper. theory, 27 (2007), 397-412.}] and {\it Englis} [{\it M. Engli$\check{s}$, Toeplitz Operators and Localization Operators, Trans. Am. Math Society 361 (2009) 1039-1052.}] states that any {\it Gabor-Daubechies} operator with window $\psi$ and symbol ${\bf a}(x,\omega)$ quantized on the phase space by a {\it Berezin-Toeplitz} operator with window $\Psi$ and symbol $\sigma(z,\bar{z})$ coincides with a {\it Toeplitz} operator with symbol $D\sigma(z,\bar{z})$ for some polynomial differential operator $D$. Using the Berezin quantization approach, we will extend the proof for polyanalytic Fock spaces. While the generation is almost mimetic for two-windowed localization operators, the Gabor analysis framework for vector-valued windows will provide a meaningful generalization of this conjecture for {\it true polyanalytic} Fock spaces and moreover for polyanalytic Fock spaces. Further extensions of this conjecture to certain classes of Gel'fand-Shilov spaces will also be considered {\it a-posteriori}.Comment: 23 page

Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle

With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework with Lie-algebraic symmetries. The exponential generating function ({\bf EGF}) carrying the {\it continuum} Dirac operator D=\sum_{j=1}^n\e_j\partial_{x_j} together with the Lie-algebraic representation of raising and lowering operators acting on the lattice h\BZ^n is used to derive the corresponding hypercomplex polynomials of discrete variable as Appell sets with membership on the space Clifford-vector-valued polynomials. Some particular examples concerning this construction such as the hypercomplex versions of falling factorials and the Poisson-Charlier polynomials are introduced. Certain applications from the view of interpolation theory and integral transforms are also discussed.Comment: 24 pages. 1 figure. v2: a major revision, including numerous improvements throughout the paper was don

Intra-Industry Trade and Revealed Comparative Advantage: An Inverted-U Relationship

This paper investigates the relationship between all types of intra-industry trade (IIT) and comparative advantage. The paper finds strong evidence of an inverted-U relationship.The results also suggest that relative autarky costs is a common determinant for any type of IIT, which contradicts the prediction made by theory for separating the determinants of horizontal and vertical IIT.intra-industry trade; horizontal intra-industry trade; vertical intra-industry trade; comparative advantage.

Fischer Decomposition for Difference Dirac Operators

We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a Fischer decomposition for the discrete Laplacian

Effects of Immigration on Intra-Industry Trade: A logit analysis

This study estimates the effects of the immigration stock, as well as those of immigrants’ characteristics, such as having the same language as that of the host country and the level of qualification or entrepreneurship, on Portuguese intra-industry trade (IIT) by types, controlling for the effects of other socio-economic factors, like economic dimensions, price indexes and distance. In addition to the member-countries of the EU-27, the group of countries studied includes five African countries with Portuguese as their official language, known as the PALOPs, and the BRIC countries. Since indexes are fractional variables, the pseudo-likelihood Logit estimator was used on the panel data to obtain the empirical results. The study found that an increase of the immigrant stock will produce an increment in the trade indexes considered and this effect is enhanced if immigrants originate from a country where Portuguese is the official language, or if they are highly qualified, whereas immigrant entrepreneurs have no significant effect.Immigration; trade; skills; entrepreneurship; panel data; Portugal. Classification-C33, F11, F12, F22.