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Lp Markov–Bernstein Inequalities on All Arcs of the Circle

2002
*
Journal of Approximation Theory
*

Introduction and Results

doi:10.1006/jath.2002.3675
fatcat:ycg2ee26xjdflmtqvbjfteinwq
*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

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

2001
*
Journal of Approximation Theory
*

We prove that for trigonometric polynomials s n

doi:10.1006/jath.2000.3502
fatcat:nchlsslmkreahoqkiyo6eskoiq
*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]

2018
*
arXiv
*
pre-print

We obtain

arXiv:1808.01273v2
fatcat:qkfo7wnlaffa5k6xruu5obibhq
*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]

2022
*
arXiv
*
pre-print

In this note we will describe a simple and practical approach to get rigorous bounds

arXiv:2012.07083v3
fatcat:dgdiwbecubcabcjs2msmetqvye
*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

1970
*
Journal of Functional Analysis
*

It is possible to deduce from these

doi:10.1016/0022-1236(70)90068-6
fatcat:hzt2kbseqvbfxkiuonbsne426y
*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

2007
*
SIAM Journal on Numerical Analysis
*

To discretize

doi:10.1137/050647414
fatcat:x2q7seocrnd6tiuclnkktlyro4
*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

doi:10.1093/imanum/dri037
fatcat:yvnmilfkmrcvxli33o4urdizaq
*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

1948
*
Bulletin of the American Mathematical Society
*

any

doi:10.1090/s0002-9904-1948-09093-0
fatcat:zmjkl55lgjhvfl5kdcms7yg6cu
*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]

2011
*
Methods of Geometric Analysis in Extension and Trace Problems
*

A new approach based

doi:10.1007/978-3-0348-0209-3_2
fatcat:ydj4quusdfbytmq6h5renaa4um
*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

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]

2012
*
arXiv
*
pre-print

In this work we present strong asymptotics

arXiv:1205.4480v1
fatcat:efnaip5exzhrplw3oduhunawci
*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]

2005
*
Lecture Notes in Computer Science
*

We study a fluid system with single

doi:10.1007/11551188_19
fatcat:gtzi5u6emvfyxea3zbklobnvom
*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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