Vector-valued L p-convergence of orthogonal series and Lagrange interpolation. Abstract We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of L p-functions in terms of Jacobi polynomi...

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic quantizable manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-value...

In this paper, we consider the problem of solving systems of fuzzy relation equations in a space with fuzzy preorder. Two types of these systems with different compositions are considered. New solvability criteria are proposed for systems of both types. The new criteria are weaker than all the known ones that are based on the assumption that fuzzy sets on the left-hand side of a system establis...

Set-valued ordered information systems can be classified into two categories: disjunctive and conjunctive systems. Through introducing two new dominance relations to set-valued information systems, we first introduce the conjunctive/disjunctive set-valued ordered information systems, and develop an approach to queuing problems for objects in presence of multiple attributes and criteria. Then, w...

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-valued function. ...

Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defi...

Set-valued information systems are generalized models of single-valued information systems. Its semantic interpretation can be classified into two categories: disjunctive and conjunctive. We focus on the former in this paper. By introducing four types of dominance relations to the disjunctive set-valued information systems, we establish a dominance-based rough sets approach, which is mainly bas...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

A multi-valued version of CTL∗ (mv-CTL∗), where both the propositions and the accessibility relation are multi-valued, taking values in a complete lattice with a complement, is considered. Contrary to all the existing model checking results for multi-valued modal logics, our lattices are not required to be finite. A set of restrictions is provided under which there is a direct translation from ...