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

Commutators on Fock spaces

Given a weighted $\ell^2$ space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond-Leontiev derivatives. This general class of operators includes many known examples, like classic fractional derivatives and Dunkl operators. This allows us to establish a general framework which goes beyond the classic Weyl-Heisenberg algebra. Concrete examples for its application are provided

q-rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels

Generalized qq-Fock spaces and structural identities

Using $q$-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their $q$-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.Comment: References added to the q-Stirling number

Generalized q-Fock Spaces and Structural Identities

Using -calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their -calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative

The price of tumor control

Ipilimumab, a cytotoxic T-lymphocyte antigen-4 (CTLA-4) blocking antibody, has been approved for the treatment of metastatic melanoma and induces adverse events (AE) in up to 64% of patients. Treatment algorithms for the management of common ipilimumab-induced AEs have lead to a reduction of morbidity, e.g. due to bowel perforations. However, the spectrum of less common AEs is expanding as ipilimumab is increasingly applied. Stringent recognition and management of AEs will reduce drug-induced morbidity and costs, and thus, positively impact the cost-benefit ratio of the drug. To facilitate timely identification and adequate management data on rare AEs were analyzed at 19 skin cancer centers. Patient files (n = 752) were screened for rare ipilimumab-associated AEs. A total of 120 AEs, some of which were life-threatening or even fatal, were reported and summarized by organ system describing the most instructive cases in detail. Previously unreported AEs like drug rash with eosinophilia and systemic symptoms (DRESS), granulomatous inflammation of the central nervous system, and aseptic meningitis, were documented. Obstacles included patientś delay in reporting symptoms and the differentiation of steroid-induced from ipilimumab-induced AEs under steroid treatment. Importantly, response rate was high in this patient population with tumor regression in 30.9% and a tumor control rate of 61.8% in stage IV melanoma patients despite the fact that some patients received only two of four recommended ipilimumab infusions. This suggests that ipilimumab-induced antitumor responses can have an early onset and that severe autoimmune reactions may reflect overtreatment. The wide spectrum of ipilimumab-induced AEs demands doctor and patient awareness to reduce morbidity and treatment costs and true ipilimumab success is dictated by both objective tumor responses and controlling severe side effects