It is proved that if such an operator is bounded, then its symbol is a polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type model for composition operators with linear symbols is established. As a consequence, explicit formulas for their polar decomposition, Aluth...
We prove that, under some general assumptions, a generator of any uniformly continuous Nemytskii operator, mapping a subset of space of bounded variation functions in the sense of Wiener into another space of this type, must be an affine function. As a special case, we obtain an earlier res...
1 defines an affine map over the infinite prism of t1 (represented in blue with dotted lines), mapping p to 1(p). The resulting 1 (p) is projected onto the local coordinates of 2, landing on triangle t2, from which it is mapped by the affine ma...
Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 5, 65–80 (2010). Article MathSciNet MATH Google Scholar Nelson, B. E., Ford, E. B. & Payne, M. J. RUN DMC: an efficient, parallel code for analyzing radial velocity observations using N-body integrations ...