Stochastic Comparability and Dual Q-Functions

On q-Quasiadditive and q-Quasimultiplicative Functions

In this paper, we introduce the notion of q-quasiadditivity of arithmetic functions, as well as the related concept of q-quasimultiplicativity, which generalise strong q-additivity and -multiplicativity, respectively. We show that there are many natural examples for these concepts, which are characterised by functional equations of the form f(qk+ra+b) = f(a)+f(b) or f(qk+ra+b) = f(a)f(b) for al...

Multiplying Schur Q-functions

Generalized Q-functions

The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ〉〈σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ〉 is ...

(P, Q)-Special Functions

It is suggested that the (p, q)-hypergeometric series studied by Burban and Klimyk (in Integral Transforms and Special Functions 2 (1994) 15-36) can be considered as a special case of a more general (P, Q)-hypergeometric series. 1. Introduction I propose a general (P, Q)-hypergeometric series. In this, I am inspired mainly by the paper of Burban and Klimyk [1] titled " P, Q-differentiation, P, ...

Q-valued Functions Revisited

Abstract. In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R) of unorderedQ-tuples of points in R. In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Qvalued functions, of their Hölder regularity and of the dimension estimate of their singular set; • we propose an alternative intrinsic ...