Search results for "polynomials"
showing 10 items of 144 documents
A multilinear Lindenstrauss theorem
2006
Abstract We show that the set of N -linear mappings on a product of N Banach spaces such that all their Arens extensions attain their norms (at the same element) is norm dense in the space of all bounded N -linear mappings.
Interpolation and approximation in L2(γ)
2007
Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…
Pietsch's factorization theorem for dominated polynomials
2007
Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.
The convolution operation on the spectra of algebras of symmetric analytic functions
2012
Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.
Multialternating graded polynomials and growth of polynomial identities
2012
Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
2007
We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
Эмануэль Гринберг - выдающиеся достижения в прикладной математике: радио-фильтры, корпуса танкеров, графы и интегральные схемы Emanuels Grinbergs - i…
2018
The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation of radio filters (1949-1959), hull of tanker calculations (1962-1964), the study of graph theory and the proof of the Grinberg theorem (1968), designing of integrated circuits (1968-1980). Calculations of radio filters are associated with the expansion of the use of continued fractions for the analysis of linear electric circuits (the Kauer model) and the developing of new tools – the Grinberg brackets (as an extension of the Euler brackets)…
Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies
2017
peer-reviewed The increasing use of composite materials for lightweight structural applications and the extended tailoring capabilities offered by variable stiffness laminates requires rapid and robust analysis tools that adequately describe the mechanical behaviour of such structures. In this work, a Rayleigh–Ritz solution for generally restrained multilayered stiffened variable angle tow plates in the post-buckling regime is presented. The plate model is based on first-order shear deformation theory and accounts for geometrical nonlinearity through von Kármán’s assumptions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed…
Estimation of ordered response models with sample selection
2011
We introduce two new Stata commands for the estimation of an ordered response model with sample selection. The opsel command uses a standard maximum-likelihood approach to fit a parametric specification of the model where errors are assumed to follow a bivariate Gaussian distribution. The snpopsel command uses the semi-nonparametric approach of Gallant and Nychka (1987, Econometrica 55: 363–390) to fit a semiparametric specification of the model where the bivariate density function of the errors is approximated by a Hermite polynomial expansion. The snpopsel command extends the set of Stata routines for semi-nonparametric estimation of discrete response models. Compared to the other semi-n…