A smooth map f: M ! N between semi-riemannian manifolds is called a harmonic morphism if f pulls back harmonic functions (i.e., local solutions of the Laplace{Beltrami equation) on N into harmonic functions on M. It is shown that a harmonic morphism is the same as a harmonic map which is moreover horizontally weakly conformal, these two notions being likewise carried over from the riemannian ca...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

It’s widely recognized that compression is useful and even necessary for inductive learning, where a short description will capture the ‘regularities’. We introduce complexitypreserving functions that preserve these regularities of the concept. They are based on the universal information distance [Bennett et al. ‘97] and define for an instance a set of elements sharing the same complexity type....

We study measure-preserving functions between Lebesgue measurable subsets of the real line. We use particular bijections of the interval [0, 1), called shifts, to approximate from below the set of measure-preserving maps on [0, 1). This construction is similar to the method used in ergodic theory to obtain special transformations by cutting and stacking. In our approach we provide the set of sh...

Using a simple basis of rational polynomial-like functions P0, . . . , Pn−1 for the free module of functions Z/nZ → Z/mZ, we characterize the subfamily of congruence preserving functions as the set of linear combinations of the products lcm(k)Pk where lcm(k) is the least common multiple of 2, . . . , k (viewed in Z/mZ). As a consequence, when n ≥ m, the number of such functions is independent o...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...