On Bernstein's inequality for entire functions of exponential type

Rahman, Q. I.; Tariq, Q. M.

doi:10.1016/j.jmaa.2009.05.035

Cited by 12 publications

(6 citation statements)

References 20 publications

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“…(18) is not as simple as in 2D, this step is skipped. As in the 2D case, the value of μ max , μ med and μ min used in (18) and (19) can only be estimated from the finite set of projections. Nevertheless, thanks to Proposition 3, which is still valid in 3D, we can neglect the errors on μ max , μ med and μ min .…”

Section: Estimation Of Angular Difference In 3dmentioning

confidence: 99%

“…The neighbors of each projection are found using the Hu moment thresholds defined in Eq. (19). The angular differences between these neighboring projections are then estimated using Formula (18).…”

Section: Noiseless Casementioning

confidence: 99%

“…Recall of Bernstein's Inequality Theorem 1 (Bernstein's inequality [19]) Let f (x) = n i=0 a i cos(i x) + b i sin(i x), a trigonometric polynomial of degree n. We have…”

Section: Appendix 1: Proofs In 2dmentioning

confidence: 99%

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Moment-Based Angular Difference Estimation Between Two Tomographic Projections in 2D and 3D

et al. 2016

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This paper introduces a new method for estimating the angular difference between two tomographic projections belonging to a set of projections taken at unknown directions in 2D and 3D. Our method relies on the projection neighbor selection in projection moment space, the calculation of the angular differences between these neighboring projections using moment properties and a projection moment neighborhood graph. The accuracy and the robustness of our method are shown on a test database including fifty 2D and 3D gray-level images at different resolutions and with different levels of noise.

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Section: Estimation Of Angular Difference In 3dmentioning

confidence: 99%

Section: Noiseless Casementioning

confidence: 99%

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Moment-Based Angular Difference Estimation Between Two Tomographic Projections in 2D and 3D

et al. 2016

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“…There is a vast literature on Markov-Bernstein inequalities, both for polynomials [5,12,14], and entire functions of exponential type. For the latter, there are Szegő type inequalities, and sharp inequalities for various subclasses of entire functions with special properties-see [4,6,16]. In another direction, weighted Bernstein inequalities involving inner functions, and model spaces have been investigated by Baranov [2,3].…”

Section: Lp(γ)mentioning

confidence: 99%

Weighted Markov-Bernstein inequalities for entire functions of exponential type

Lubinsky

2014

Publ Inst Math (Belgr)

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We prove weighted Markov-Bernstein inequalities of the form ∞ −∞ |f ′ (x)| p w(x) dx C(σ + 1) p ∞ −∞ |f (x)| p w(x) dx Here w satisfies certain doubling type properties, f is an entire function of exponential type σ, p > 0, and C is independent of f and σ. For example, w(x) = (1 + x 2) α satisfies the conditions for any α ∈ R. Classical doubling inequalities of Mastroianni and Totik inspired this result.

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“…This classical and important inequality was extended by many authors in many different directions. It is impossible to give an exhaustive list of references, but we would like to mention [9,22,32,34,35,40] and [26,Lecture 28].…”

Section: Introductionmentioning

confidence: 99%

Weighted norm inequalities for de Branges-Rovnyak spaces and their applications

Baranov¹,

Fricain²,

Mashreghi³

2010

ajm

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Let H(b) denote the de Branges-Rovnyak space associated with a function b in the unit ball of H ∞ (C + ). We study the boundary behavior of the derivatives of functions in H(b) and obtain weighted norm estimates of the form f (n)and µ is a Carleson-type measure on C + ∪ R. We provide several applications of these inequalities. We apply them to obtain embedding theorems for H(b) spaces. These results extend Cohn and Volberg-Treil embedding theorems for the model (star-invariant) subspaces which are special classes of de Branges-Rovnyak spaces. We also exploit the inequalities for the derivatives to study stability of Riesz bases of reproducing kernels {k b λn } in H(b) under small perturbations of the points λ n . 2000 Mathematics Subject Classification. Primary: 46E15, 46E22, Secondary: 30D55, 47A15. Key words and phrases. Bernstein's inequality, de Branges-Rovnyak space, model subspace, reproducing kernel, embedding theorem, Riesz basis. This work was supported by funds from NSERC (Canada), Jacques Cartier Center (France) and RFBR (Russia).

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On Bernstein's inequality for entire functions of exponential type

Cited by 12 publications

References 20 publications

Moment-Based Angular Difference Estimation Between Two Tomographic Projections in 2D and 3D

Moment-Based Angular Difference Estimation Between Two Tomographic Projections in 2D and 3D

Weighted Markov-Bernstein inequalities for entire functions of exponential type

Weighted norm inequalities for de Branges-Rovnyak spaces and their applications

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