G. Szego. Orthogonal polynomials, volume 33 of Amer. Math. Soc. Colloq. Publ. Amer. Math. Soc., Providence, Rhode Island, 3rd edition, 1967. Home/Search Document Not in Database Summary Related Articles Check |
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Universality for Eigenvalue Correlations at the Origin of.. - Kuijlaars, Vanlessen (Correct)
....n,m (y 1 , y m ) det(K n (y i , y j ) 1#i,j#m , n 1 p j,n (x)p j,n (y) # n 1,n # n,n p n,n (x)p n 1,n (y) p n 1,n (x)p n,n (y) 1.3) which gives the connection with orthogonal polynomials. The second equality in (1. 3) follows from the Christo#el Darboux formula [35]. Akemann et al. 2] showed that the local eigenvalue correlations at the origin of the spectrum have a universal behavior, described in terms of the following Bessel kernel # (u, v) # # u # v , 1.4) where J # denotes the usual Bessel function of order # . In [2] it was ....
G. Szego, " Orthogonal Polynomials," 4th ed., Amer. Math. Soc. Providence RI, 1975.
On the Asymptotic Density of Tautologies in Logic of.. - Marek Zaionc Computer (Correct)
....[1] Also see [2] for the presentation of this method in logics. Many questions concerning the asymptotic behavior of a sequence A can be e#ciently resolved by analyzing the behavior of generating function f A at the complex circle = R. The key tool will be the following result due to Szego [5] [Thm. 8.4] see as well [6] Thm. 5.3.2] which relates the generating functions of numerical sequences with limit of fractions. For the technique of proof described below please consult also [2] We need the following much simpler versions of the Szego Lemma with one and two singularities Lemma ....
Szego, G. (1975) Orthogonal polynomials. Fourth edition.AMS, Colloquium Publications, 23, Providence.
Computation of Gauss-Kronrod Quadrature Rules - Calvetti, Golub, Gragg, Reichel (2 citations) (Correct)
....# 0 , b # 1 , a # 1 , for the orthogonal polynomials with respect to the measure (4.4) When dw is a measure of Jacobi type dw(x) c 0 (b dx, a x b, #, # (4. 7) then so is dw # , and explicit formulas for the recursion coe#cients a # j and b # j are available; see, e.g. [16]. The scaling factor c 0 , where c 1 0 : b # # 1 B(# 1, # 1) 4.8) and B denotes the beta function, secures that 0 = 1. When dw is not of Jacobi type and recursion coe#cients a j and b j for orthogonal polynomials associated with the measure dw are available, a scheme by Golub and ....
....rules associated with Jacobi measures dw(x) c 0 (1 (1 x) dx, x 1, #, # (5.1) where the scaling factor c 0 , given by (4.8) with a = and b = 1, is chosen to make 0 = 1. Recursion coe#cients for the associated orthogonal polynomials are explicitly known; see, e.g. [16]. Our computational results can be summarized as follows. For many choices of # and # in (5.1) both Laurie s and our methods yield high accuracy. However, when at least one of the exponents in (5.1) is fairly close to our method generally gives 16 D. Calvetti et al. Errors in computed ....
G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Society, Providence, 1975.
Numerical Methods for Accurate Finite Element Solutions of.. - Kim, Lee, Oh (2002) (Correct)
....it was pointed out at the outset of this section, u fe (x) is not a polynomial, but u fe and u # fe are polynomials. Hence ds u # fe (s) is a polynomial of the variable s. Thus, the best L approximation of the mapping technique is given by the partial sum of Jacobi polynomial expansion(see [25]) If the exact solution u ex #1 (x) is x (# 1 2) then b ds, 3.3) where n (s) x 1 (3.4) and (3.5) 7 is the generalized Fourier coe#cients in the orthogonal expansion of (s 1) by Jacobi polynomials. ....
....n (s) x 1 (3.4) and (3.5) 7 is the generalized Fourier coe#cients in the orthogonal expansion of (s 1) by Jacobi polynomials. Since n (s) 3.6) we obtain ds (3.7) # ds. By (p. 68 of [25]) we have . 3.8) Hence, the generalized Fourier coe#cients a n can be written as follows: a n = ## # = ds. Applying Lemma 3.1, we have a n = 1 ## = Since ....
Szego, G. : Orthogonal Polynomials, AMS Colloq. Public. Vol. 23, 4th ed. 1975.
Para-Orthogonal Polynomials in Frequency Analysis - Daruis, Njåstad, Van.. (2002) (Correct)
....coe#cient # n ) with respect to #N . Then we have # n (#N , z) # n # n (#N , z) 1.3) n = j (#N , 0) 1 2 . 1.4) # The third author s research is supported by INTAS 00 272 and research grant G.0184.02 of FWOVlaanderen. For the basic theory of Szego polynomials, see e.g. [1, 2, 7, 18, 19]. Let k : k = 1, 2, n 0 be a numbering of the so called frequency points e ; j = 1, 2, I , and set # k = Let # be the discrete measure defined by #(#) # k #(e # k ) 1.5) Then the measures #N N converge in the weak# sense to # (see [6, 15] ....
....n (#N , z) N = 1, 2, itself converges to a polynomial B n (z) with distinct zeros, then (3.6) 3.7) holds. We consider the signal x(m) # #mi 2 e #mi 2 , # 0. 3.8) The frequency points are # 1 = i and # 2 = i. By using the Szego recursion formulas (see, e.g. [7, 18]) it can be shown that for n = 3, 4, 5 the para orthogonal polynomials B n (#N , z) converge to the polynomial B n (#, z) z #) z i) z i) 3.9) Let n = 3 and # = 1. Then in addition to the frequency points # 1 and # 2 , the polynomial B n ( 1, z) has the zero # 3 = 1. By a ....
G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, Providence RI, 1975 (4th edition)
Computing the Poles of Autoregressive Models from the.. - Ammar, Calvetti, Reichel (Correct)
....are also called Levinson polynomials and backward predictor polynomials in the engineering literature. Szego polynomials can be recursively computed using the well known Levinson Durbin algorithm. This algorithm is equivalent with the use of the recursions formulas introduced by Szego (see, e.g. [21, 15]) to construct the coefficients of the Szego polynomials in the power basis. In particular, the Szego recursions for constructing the monic polynomials j are given by j 1 ( j ( fl j 1 j 1 ( fl j 1 j ( where 0 ( 0 ( 1, and fl j 1 = Gamma 1; j = j ; ....
G. Szego. Orthogonal Polynomials. American Math. Soc., Providence, 1939.
Multiplicative Renormalization And Generating Functions I. - Asai, Kubo, Kuo (2002) (Correct)
....are called Szego Jacobi parameters of . A generating function for the polynomials is a function of the form a n P n (x)t , 1.2) where a n s are constants. There is an enormous amount of literature on orthogonal polynomials and generating functions, see for example the books [6] 7] 9] [11]. Given such a probability measure , the computation of polynomials P n s by using the Gram Schmidt orthogonalization process is in fact impractical and very hard, if not impossible. On the other hand, suppose we have a generating function #(t, x) for like in Equation (1.2) Then by expanding ....
Szego, M.: Orthogonal Polynomials. Coll. Publ. 23, Amer. Math. Soc., 1975
Approximation of Conformal Mapping via the Szegö Kernel Method - Pritsker (2003) Self-citation (Szego) (Correct)
....with bounded boundary rotation (Radon domains) piecewise smooth and smooth domains (cf. Pommerenke [17, Chap. 7] Applying Gram Schmidt orthonormalization to monomials # n=0 in the Smirnov domain G, we obtain a complete orthonormal system of polynomials n (z) # n=0 in E 2 (G) see Szego [21]) Next, we introduce the Szego kernel p k (#)p k (z) z, # where convergence of this bilinear series is uniform in z and # on compact subsets in G [21] 19] 7] The importance of the Szego kernel lies in its reproducing property f(#) f(z)K(z, #) which holds for any f E 2 (G) ....
.... to monomials # n=0 in the Smirnov domain G, we obtain a complete orthonormal system of polynomials n (z) # n=0 in E 2 (G) see Szego [21] Next, we introduce the Szego kernel p k (#)p k (z) z, # where convergence of this bilinear series is uniform in z and # on compact subsets in G [21], 19] 7] The importance of the Szego kernel lies in its reproducing property f(#) f(z)K(z, #) which holds for any f E 2 (G) Equivalently, every f E 2 (G) can be represented by its Fourier series (1.2) f(#) a k p k (#) k=0 # f(z)p k (z) p k (#) convergent in the ....
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G. Szego, Orthogonal Polynomials, Amer. Math. Soc., Providence, 1975.
Mass Points Of Measures And Orthogonal Polynomials On The Unit.. - Golinskii Self-citation (Szego) (Correct)
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G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence,
On the convergence of multipoint Padé-type.. - Bultheel.. (Correct)
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G. Szego. Orthogonal polynomials, volume 33 of Amer. Math. Soc. Colloq. Publ. Amer. Math. Soc., Providence, Rhode Island, 3rd edition, 1967.
Unknown - (Correct)
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G. Szego, Orthogonal Polynomials, Vol. 23 (third edition), Amer. Math. Soc., Providence, RI, 1967.
Generalized Hypergroups and Orthogonal Polynomials - Lasser, Obermaier, Rauhut (2005) (Correct)
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G. Szego, 'Orthogonal polynomials', Amer. Math. Soc., New York, 1959.
Two Asymptotic Series - Finch (2003) (Correct)
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G. Szego, Orthogonal Polynomials,2 nd ed., Amer. Math. Soc., 1975, pp. 205---206; MR0106295 (21 #5029).
Computation of Gauss-Kronrod Quadrature Rules with.. - Ammar, Calvetti, Reichel (Correct)
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G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Society, Providence, 1975.
Computation of Gauss-Kronrod Quadrature Rules with.. - Ammar, Calvetti, Reichel (Correct)
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G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Society, Providence, 1975.
Derivatives of Faber polynomials and Markov inequalities - Pritsker (Correct)
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G. Szego, "Orthogonal Polynomials," Amer. Math. Soc., Providence, 1975.
A Mehler-Heine type formula for Hermite-Sobolev.. - Castano-Garcia.. (Correct)
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G. Szego, Orthogonal Polynomials, (Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, RI, 1975(4th edition)). 11
Zeros Of Gegenbauer And Hermite Polynomials And Connection.. - Area, Dimitrov, Al. (Correct)
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G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Coll. Publ., Vol. 23, Providence, RI, 1975.
Multiplicative Renormalization And Generating Functions Ii. - Asai, Kubo, Kuo (2003) (Correct)
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Szego, M.: Orthogonal Polynomials. Coll. Publ. 23, Amer. Math. Soc., 1975
On An Inverse Eigenproblem For Jacobi Matrices - Calvetti And Reichel (Correct)
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G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Society, Providence, 1975.
Necessary and Sufficient Condition that the Limit of.. - Geronimo, Hill (2002) (Correct)
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G. Szego, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 23 (1975), 4th Ed., Providence.
Incremental Construction of Projection Generalizing Neural.. - Sugiyama, Ogawa (2002) (Correct)
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G. Szego, Orthogonal Polynomials, Amer. Math. Soc., Providence, Rhode Island, 1939.
A renormalized Riesz potential and applications - Putinar (Correct)
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Szego, G., Orthogonal polynomials, Amer. Math. Soc., Providence, R. I., 1939.
Orthogonal Polynomials For A Family Of Product Weight Functions On.. - Xu (1997) (4 citations) (Correct)
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H. Szego, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Providence, RI, 1975.
Continuation Methods For The Computation Of Zeros Of.. - Ammar, Calvetti, Reichel (Correct)
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G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Soc., Providence, 1975.
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