Related papers: Characteristic functions and Colligations
Scaling-invariant functions preserve the order of points when the points are scaled by the same positive scalar (with respect to a unique reference point). Composites of strictly monotonic functions with positively homogeneous functions are…
In deformation quantization one can associate five characteristic functions to (stable) formality morphisms on cochains and chains and to "two-brane" formality morphisms. We show that these characteristic functions agree.
In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…
We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on $n$ bits that are induced from Boolean functions on $k$ bits, for $k\leq n$. We consider such transformations that are not…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
We characterize which graph invariants are partition functions of a spin model over the complex numbers, in terms of the rank growth of associated `connection matrices'.
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
Two simple observations are made: (1) If the normal function associated to a Hodge class has a zero locus of positive dimension, then it has a singularity. (2) The intersection cohomology of the dual variety contains the cohomology of the…
In previous work, we have introduced and studied a lifting property in congruence--distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean…
The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…
The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…
The class of $\mu$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class…
A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling…
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\ow)^{-1}$ for $|z|, |w| < 1$, by means of…
Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the…
Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…