Quantizations from reproducing kernel spaces

The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L2(C,d2z/π) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s. We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s-dependent quantizations is also considered. ► We discuss in detail an interesting decomposition of L2, in terms of ladder operators. ► We consider coherent states on this structure and we use them for quantization. ► We show how this structure is related with non hermitian quantum mechanics. ► We consider the relation between different schemes of quantizations.