Function Space

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, G/H. We develop normal mode expansions on the internal manifold and show that the conventional ...

Given an operator L acting on a function space, the J-matrix method consists of finding a sequence y_n of functions such that the operator L acts tridiagonally on y_n with respect to n. Once such a tridiagonalization is obtained, a number of characteristics of such an operator L can be obtained. In particular, information on eigenvalues and eigenfunctions, bound states, spectral decompositions, etc. can be obtained in this way. We review the general set-up, and we discuss two examples in detail; the Schrodinger operator with Morse potential and the Lame equation.

We show that the inclusion of topological lagrangians in non-linear sigma models introduces certain topological non-trivial abelian background fields in the configuration space of these theories. In particular, the Hopf and the Wess-Zumino terms lead, respectively, to a vortex and a monopole in the corresponding configuration space for 2+1 and 3+1 dimensional theories. That topological solitons acquire anomalous spin and

In this seminar we try to explain why the Drury-Arveson space is important in operator theory, why it is interesting from the viewpoint of several complex variables, how it is related to the sub-Riemannian geometry of the Heisenberg group. We do this by ...

Elements based purely on completeness and continuity requirements perform erroneously in a certain class of problems. These are called the locking situations, and a variety of phenomena like shear locking, membrane locking, volumetric locking, etc., have been identified. Locking has been eliminated by many techniques, e.g. reduced integration, addition of bubble functions, use of assumed strain approaches, mixed and hybrid approaches, etc. In this paper, we review the field consistency paradigm using a function space model, and propose a method to identify field-inconsistent spaces for projections that show locking behaviour. The case of the Timoshenko beam serves as an illustrative example. Copyright © 2001 John Wiley & Sons, Ltd.

Gram Schmidt orthonormalization procedure is an important technique to get a set of orthonormal linearly independent set of vectors from a given set of linearly independent vectors, which are not orthonormal.  As an illustration, the set of Legendre polynomials is generated as the orthonormal set of functions in the function space spanned by linearly independent set of functions, {1,x,x^2,    … x^N…∞} in the interval {-1,1}.

The functional space covered by the conjunctions and and but in English is divided between three conjunctions in Russian: i ‘and,’ a ‘and, but’ and no ‘but.’ We analyse these markers as topic management devices, i.e. they impose different kinds of constraints on the discourse topics (questions under discussion) addressed by their conjuncts. This paper gives a detailed review of the observations from descriptive literature on the distribution of these markers in light of the proposed underlying classification of questions, and shows that our theoretical approach provides a uniform explanation to a large variety of their uses, as well as to the existing equivalences and non-equivalences between the Russian and the English counterparts.

Suppose that (M,d,m) is an unbounded metric measure space, which possesses two geometric properties, called "isoperimetric property" and "approximate midpoint property", and that the measure m is locally doubling. The isoperimetric property implies that the volume of balls grows at least exponentially with the radius. Hence the measure m is not globally doubling. In this paper we define an atomic

In this article we study metric measure spaces with variable dimension. We consider Lebesgue spaces on these sets, and embeddings of the Riesz potential in these spaces. We also investigate Hajłasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.

We study BMO spaces associated with semigroup of operators and apply the results to boundedness of Fourier multipliers. We prove a universal interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative Lp spaces for all 1 < p < \infty, with optimal constants in p.