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Characterizations of differentiability for h-convex functions in stratified groups
subdifferential stratified groups second order differentiability
2010/12/14
Using the notion of h-subdifferential, we characterize both first and second order differentiability of h-convex functions in stratified groups. We show that Aleksandrov’s second order differentiabili...
Brown (1980, 1981) proved that the renewal function is concave if the inter-renewal istribution
is DFR (decreasing failure rate), and conjectured the converse. This note settles Brown’s conjecture wi...
A Pieri formula for Macdonald's spherical functions and polynomials
symmetric functions Hall-Littlewood polynomials Macdonald poly-nomials Pieri formulas root systems
2010/12/10
We present explicit Pieri formulas for Macdonald’s spherical func-tions (or generalized Hall-Littlewood polynomials associated with root sys-tems) and their q-deformation the Macdonald polynomials. Fo...
Vector Spaces of Non-measurable Functions
lineability spaceability non-measurable functions density character
2007/12/10
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensio...