Positive Definiteness of Complex Piecewise Linear Functions and Some of Its Applications

Zastavnyi, V. P.; Manov, Anatoliy

doi:10.1134/s0001434618030227

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эпоха чебышева и братьев марковых1

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2021

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“…Заставным и А.Д. Мановым [132]. На случай однородных пространств 𝑀 = 𝐺/𝐻 порядковое неравенство Бернштейна изучалось И.З.…”

Section: эпоха чебышева и братьев марковыхunclassified

Sharp Bernstein-Nikolskii inequalities for polynomials and entire functions of exponential type

Горбачев

2021

Chebyshevskii Sbornik

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The classical Bernstein-Nikolskii inequalities of the form ‖𝐷𝑓 ‖ 𝑞 𝒞 𝑝𝑞 ‖𝑓 ‖ 𝑝 for 𝑓 ∈ 𝑌 , give estimates for the 𝑝𝑞-norms of the differential operators 𝐷 on classes 𝑌 of polynomials and entire functions of exponential type. These inequalities play an important role in harmonic analysis, approximation theory and find applications in number theory and metric geometry. Both order inequalities and inequalities with sharp constants are studied. The last case is especially interesting because the extremal functions depend on the geometry of the manifold and this fact helps in solving geometric problems.

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Section: эпоха чебышева и братьев марковыхunclassified

Sharp Bernstein-Nikolskii inequalities for polynomials and entire functions of exponential type

Горбачев

2021

Chebyshevskii Sbornik

View full text Add to dashboard Cite

show abstract

Positive Definiteness of Complex Piecewise Linear Functions and Some of Its Applications

Cited by 1 publication

References 8 publications

Sharp Bernstein-Nikolskii inequalities for polynomials and entire functions of exponential type

Sharp Bernstein-Nikolskii inequalities for polynomials and entire functions of exponential type

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