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### Lp Markov–Bernstein Inequalities on All Arcs of the Circle

C.K. Kobindarajah, D.S. Lubinsky
2002 Journal of Approximation Theory
Introduction and Results The classical Markov-Bernstein inequality for trigonometric polynomials s n ( ) := n X j=0 (c j cos j + d j sin j ) of degree n is ks 0 n k L1[0;2 ] nks n k L1[0;2 ] : The same  ...  Then there is the sharp inequality What are the L p analogues? This question arose originally in connection with large sieve inequalities [7] , on subarcs of the circle.  ...

### Markov and Bernstein type inequalities for polynomials

NK Govil, RN Mohapatra
1999 Journal of Inequalities and Applications
Markov proved that if p(z) =0 a z is a real polynomial of degree n, then The above inequality which is known as Markov's Inequality is best possible and becomes equality for the Chebyshev polynomial T"  ...  Few years later, Serge Bernstein needed the analogue ofthis result for the unit disk in the complex plane instead of the interval [-1, 1] and the following is known as Bernstein's Inequality.  ...  In Section 2, we discuss some of the generalizations and refinements of the Bernstein and Markov inequalities while in Section 3, Bernstein type inequalities for polynomials having no zeros in a circle  ...

### Lp Markov–Bernstein Inequalities on Arcs of the Circle

D.S. Lubinsky
2001 Journal of Approximation Theory
We prove that for trigonometric polynomials s n of degree n, we have  ...  &: : |P(e i% )| p d%. (19) (IX ) We Establish (18) for p>1 We note that inequalities like (18) are an essential ingredient of the procedure used in [8, 9] for proving weighted Markov Bernstein inequalities  ...  Now if all zeros of P lie on 2, then we may define a single valued branch of g of (20) in C "2.  ...

### Dimension independent Bernstein-Markov inequalities in Gauss space [article]

Alexandros Eskenazis, Paata Ivanisvili
2018 arXiv   pre-print
We obtain the following dimension independent Bernstein-Markov inequality in Gauss space: for each 1≤ p<∞ there exists a constant C_p>0 such that for any k≥ 1 and all polynomials P on R^k we have ∇ P_L  ...  We also show that under some mild growth assumptions on any function B ∈ C^2((0,∞))∩ C([0,∞)) with B', B">0 we have ∫_R^k B( |LP(x)|) dγ_k(x) ≤∫_R^k B( 10 (degP)^α_B|P(x)|)dγ_k(x) where L=Δ-x·∇ is the  ...  We would like to thank Volodymyr Andriyevskyy for discussions that helped us to simplify the proof of Lemma 15.  ...

### Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups [article]

Mark Pollicott, Polina Vytnova
2022 arXiv   pre-print
In this note we will describe a simple and practical approach to get rigorous bounds on the Hausdorff dimension of limits sets for some one dimensional Markov iterated function schemes.  ...  As our first application we confirm, and often strengthen, conjectures on the difference of the Lagrange and Markov spectra in Diophantine analysis, which appear in the work of Matheus and Moreira arXiv  ...  The proof of Lemma 3.15 relies on the fact that for any function f analytic on a domain bounded by a Bernstein ellipse the image L t f is analytic on a larger domain bounded by another Bernstein ellipse  ...

### On analytic extension of semigroups of operators

Arne Beurling
1970 Journal of Functional Analysis
It is possible to deduce from these inequalities and the fact that all the fn coincide with f on y0 , that f coincide a.e. on this interval with an analytic function g.  ...  Let Jn denote the integral of sinn ~8 extended over [O, l] and define for fz = 1, 2,... By an inequality of S. Bernstein, J Dy sin= ~5 J < (mt)~.  ...

### BPX‐type Preconditioners for Second and Fourth Order Elliptic Problems on the Sphere

Jan Maes, Angela Kunoth, Adhemar Bultheel
2007 SIAM Journal on Numerical Analysis
To discretize the second order problem we construct C 0 linear elements on the sphere, and for the fourth order problem we construct C 1 finite elements of Powell-Sabin type on the sphere.  ...  We develop two Bramble-Pasciak-Xu-type preconditioners for second resp. fourth order elliptic problems on the surface of the two-sphere.  ...  Indeed, the inequality can be shown using the Markov inequality for polynomials ([9] ), and the inequality can be deduced, for instance, from the work in [29, Section 6.2] .  ...

### A hierarchical basis preconditioner for the biharmonic equation on the sphere

2006 IMA Journal of Numerical Analysis
In this paper we construct a C 1 continuous hierarchical basis on a sphere, and we estimate the condition number of the stiffness matrix for the biharmonic equation on the sphere preconditioned by this  ...  Furthermore we introduce a wavelet basis on the sphere for which we expect a uniformly well-conditioned and (quasi-) sparse stiffness matrix.  ...  This work is partially supported by the Flemish Fund for Scientific Research (FWO Vlaanderen) project MISS (G.0211.02), and by the Belgian Programme on Interuniversity Attraction Poles, initiated by the  ...

### General index, 1965-1974: Research announcements

1975 Bulletin of the American Mathematical Society
on the unit circle, 73, 195 .  ...  ., The bounded linear operators that commute with the Bernstein operators, 74, 111 Koppelman, Walter, The Cauchy integral for functions of several complex variables, 73, 373 , On orbits associated with  ...  ., The obstruction to fibering a manifold over a circle, 73, 737 godic flows on LP, 76, 138 Fife, Paul C. See Berger, Melvyn S. deFigueiredo, Djairo G. See Browder, Felix E.  ...

### The summer meeting in Madison

R. H. Bruck
1948 Bulletin of the American Mathematical Society
any arc s of d to the corresponding chord c satisfies the inequality s/c ^a ( = constant) ; (iv) d contain the circle | z\ <r and are contained in 121 <R.  ...  (b) It does not vanish in R except possibly at one point on the circle where F'(£) =0. (c) Along the circle If I -1, ƒ<**«<>.  ...

### Smooth Functions on Subsets of ℝ n [chapter]

Alexander Brudnyi, Yuri Brudnyi
2011 Methods of Geometric Analysis in Extension and Trace Problems
A new approach based on Whitney's inequality from [Wh-1957] and on a local Markov inequality was proposed by Yu. Brudnyi and Gopengauz [BGo-1961] , see also [BGo-1963] for the proofs.  ...  In particular, any arc of this curve is of infinite length.  ...  Local inequalities for polynomials We will prove several inequalities estimating the uniform or L p -norm of a polynomial on a convex body via that on a subset of positive measure.  ...

### The Annual meeting in Rochester

R. D. Schafer
1957 Bulletin of the American Mathematical Society
The following problem was suggested by D. Blackwell: denote the number of susceptibles and infected individuals in a population by s and i, respectively. Consider  ...  Assume that <f> and ƒ are both analytic at each point of So, that tf>'?*0 everywhere on S 0 , and that <f> does not map distinct arcs on So onto the same arc.  ...  John Wermer: Function rings on the circle.  ...

### Padé approximants to certain elliptic-type functions [article]

Laurent Baratchart, Maxim Yattselev
2012 arXiv   pre-print
In this work we present strong asymptotics of diagonal Padé approximants to f_h and describe the behavior of the spurious pole and the regions of locally uniform convergence from a generic perspective.  ...  For h be a complex-valued non-vanishing Dini-continuous function on Δ, we consider f_h(z) := (1/π i)∫_Δ h(t)/(t-z) dt/w^+(t), where w(z) := √(∏_k=0^3(z-a_k)) and w^+ the one-sided value according to some  ...  Then the norms p n ∆ are uniformly bounded and (7.10) p n (z)ϕ −n (z) ≤ const., z ∈ D, by the Bernstein-Walsh inequality.  ...

### Index: Volumes 21-30

1971 Proceedings of the American Mathematical Society
On the uniqueness of solutions of certain improperly posed problems, 24 (1970), Carl D. 1 A duality between spheres and spheres with arcs, 25 (1970), 781-785. 57A10; 54A05 Silberger, Allan J. 1 All algebras  ...  The algebra of functions with Fourier transforms in Lp, 24 (1970), 217-219.  ...

### On Fitting Finite Dirichlet Mixture Using ECM and MML [chapter]

Nizar Bouguila, Djemel Ziou
2005 Lecture Notes in Computer Science
We study a fluid system with single on/off source in which the active (on) and silent periods (off) follow General and Exponential distributions respectively.  ...  The system is analysed for different active periods corresponding to the service time of an M/G/1 queue and the busy period of an M/G/1 queue.  ...  model and the minimum of the empirical risk in the model) satisfies a Bernstein like inequality where the variance term is a function of the learning rate.  ...
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