[PDF] Top 20 Asymptotic Properties of Orthogonal and Extremal Polynomials
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Asymptotic Properties of Orthogonal and Extremal Polynomials
... of polynomials in the next section, we will apply it in the case when the orthonormal polynomials correspond to a measure supported on the closed unit disk in Section ...of asymptotic density 1 so ... See full document
116
On asymptotic properties of Laguerre–Sobolev type orthogonal polynomials
... Type Orthogonal Polynomials, where p and q are real ...of asymptotic properties of the sequence S a n ðxÞ n2N , of Laguerre–Sobolev type monic polynomials, orthogonal with ... See full document
14
On asymptotic properties of Freud–Sobolev orthogonal polynomials
... orthogonal with respect to ðÞ; such that the number of involved terms does not depend on the degree of the polynomials. Thus, we reach in a natural way the measures associated with a Freud weight. In ... See full document
16
On asymptotic properties of Freud–Sobolev orthogonal polynomials
... the polynomials, fP n g; orthogonal with respect to the measure m and the polynomials, fQ n g; orthogonal with respect to ðÞ; such that the number of involved terms does not depend on the ... See full document
16
Asymptotic properties and Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer–Sobolev inner product
... p if (2α + 1)/α < p. Now, using this and (22) and the relation (21) follows. 4. Necessary conditions for the norm convergence The problem of the norm convergence of partial sums of the Fourier expansions in terms of ... See full document
10
Asymptotic Properties of Balanced Extremal Sobolev Polynomials: Coherent Case
... these polynomials is also ...monic orthogonal polynomials sequence corresponding to a new measure constructed as a combination of + 0 and + 1 ; we conjecture that this result is valid in a more ... See full document
16
Asymptotic of extremal polynomials in the complex plane
... 1 Introduction. Sobolev orthogonal polynomials play a central role in the extension of the general theory of orthogonal polynomials. Let µ 0 , . . . , µ N be finite positive Borel measures in ... See full document
14
Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials
... the asymptotic properties of the corresponding orthog-onal polynomials and the behavior of their ...the asymptotic behavior between these Sobolev orthogonal polynomials and the ... See full document
14
Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms
... the asymptotic behavior of Sobolev orthogonal polynomials is one of the main topics of interest to investigators in the ...root asymptotic of Sobolev orthogonal polynomials when ... See full document
18
Asymptotic behaviour of Laguerre–Sobolev-type orthogonal polynomials. A nondiagonal case
... the properties of classical Laguerre polynomials which will be needed along the ...the asymptotic properties of the Laguerre–Sobolev-type polynomials, orthogonal with respect to ... See full document
10
A note on asymptotic zero distribution of orthogonal polynomials
... Abstract We strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a sequence of orthogonal polynomials {p n } ∞ n =1 for which the coefficients in the three term recurrence ... See full document
7
Asymptotic behavior and zero distribution of Carleman orthogonal polynomials
... structural properties of the sets Σ p , p ≥ 1. These properties have been previously established for different, but similarly defined ...Faber polynomials F n (z), n = 0, 1, 2, ... See full document
22
A Riemann–Hilbert approach to asymptotic questions for orthogonal polynomials
... and for weights described in Remark 1.1 above. In Section 3 we remark on how to modify the proof to treat weights of types (I) and (III). The plan of this paper is as follows.In the remainder of this section we state the ... See full document
17
Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials
... several orthogonal polynomials of the Askey table admit asymptotic expansions in terms of Hermite and Laguerre polynomials [López and Temme, ...between polynomials of the Askey table ... See full document
25
Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials
... Figure 5: Leading order terms of the orthonormal polynomials in the lens for the weight function w(x) = (1 − x 2 ) −1/2 exp( −xt) at n = 101. Figure 5 shows us that the envelope of the polynomial indeed behaves as ... See full document
39
Construction and implementation of asymptotic expansions for Jacobi--type orthogonal polynomials
... the asymptotic expansion in the left ...‘exact’ polynomials we compared with were obtained using Matlab routines from the OPQ-library that accompanies the book ...the asymptotic nature of the ... See full document
38
Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View
... of orthogonal polynomials have been introduced describing many new classes of orthogonal ...of orthogonal polynomials can be easily obtained by applying the concept of Löwdin ... See full document
6
The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights
... approach is based on the Deift–Zhou method of steepest descent applied to the Riemann–Hilbert problem for orthogonal polynomials of Fokas, Its, and Kitaev [ 12 ].. logarithm of the parti[r] ... See full document
11
Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions
... the orthogonal polynomials. In addition, even when the orthogonal polynomial exists, its zeros may not be real, and they may distribute themselves on some curve or union of curves in the complex ... See full document
44
The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis
... hypergeometric orthogonal polynomials that occur in the Askey ...how asymptotic representations can be derived by using the generating functions of the ...the asymptotic representation of the ... See full document
11
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