915 resultados para Orthogonal polynomials on the real line
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We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.
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2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35
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MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32
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We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.
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Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.
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2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.
On the Front Line: frontal zones as priority at-sea conservation areas for mobile marine vertebrates
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1.Identifying priority areas for marine vertebrate conservation is complex because species of conservation concern are highly mobile, inhabit dynamic habitats and are difficult to monitor. 2.Many marine vertebrates are known to associate with oceanographic fronts – physical interfaces at the transition between water masses – for foraging and migration, making them important candidate sites for conservation. Here, we review associations between marine vertebrates and fronts and how they vary with scale, regional oceanography and foraging ecology. 3.Accessibility, spatiotemporal predictability and relative productivity of front-associated foraging habitats are key aspects of their ecological importance. Predictable mesoscale (10s–100s km) regions of persistent frontal activity (‘frontal zones’) are particularly significant. 4.Frontal zones are hotspots of overlap between critical habitat and spatially explicit anthropogenic threats, such as the concentration of fisheries activity. As such, they represent tractable conservation units, in which to target measures for threat mitigation. 5.Front mapping via Earth observation (EO) remote sensing facilitates identification and monitoring of these hotspots of vulnerability. Seasonal or climatological products can locate biophysical hotspots, while near-real-time front mapping augments the suite of tools supporting spatially dynamic ocean management. 6.Synthesis and applications. Frontal zones are ecologically important for mobile marine vertebrates. We surmise that relative accessibility, predictability and productivity are key biophysical characteristics of ecologically significant frontal zones in contrasting oceanographic regions. Persistent frontal zones are potential priority conservation areas for multiple marine vertebrate taxa and are easily identifiable through front mapping via EO remote sensing. These insights are useful for marine spatial planning and marine biodiversity conservation, both within Exclusive Economic Zones and in the open oceans.
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Language processing plays a crucial role in language development, providing the ability to assign structural representations to input strings (e.g., Fodor, 1998). In this paper we aim at contributing to the study of children's processing routines, examining the operations underlying the auditory processing of relative clauses in children compared to adults. English-speaking children (6–8;11) and adults participated in the study, which employed a self-paced listening task with a final comprehension question. The aim was to determine (i) the role of number agreement in object relative clauses in which the subject and object NPs differ in terms of number properties, and (ii) the role of verb morphology (active vs. passive) in subject relative clauses. Even though children's off-line accuracy was not always comparable to that of adults, analyses of reaction times results support the view that children have the same structural processing reflexes observed in adults.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.
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Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1, p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C. It is shown that they are orthonormal on the real and the imaginary axes in the complex plane ...