Golden Ratio and Lebesgue Constant in Local Dirichlet Spaces

Mostafa Nasri ()
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Mostafa Nasri: University of Winnipeg, Department of Mathematics and Statistics

Chapter 81 in Operator Theory, 2026, pp 2491-2499 from Springer

Abstract: Abstract The Lebesgue constant ℒ n $$\mathcal {L}_n$$ is classically interpreted as the norm of S n $$S_n$$ , the n-th partial Taylor sum, on the disc algebra or the Lebesgue space L 1 ( 𝕋 ) $$L^1(\mathbb {T})$$ . Although numerous integral and summation formulas for ℒ n $$\mathcal {L}_n$$ exist, an exact, closed-form expression remains elusive. This concept can be extended by considering S n $$S_n$$ on various Banach spaces of functions on the open unit disc 𝔻 $$\mathbb {D}$$ , thereby defining the corresponding Lebesgue constant for each space. Lebesgue constants for local Dirichlet spaces were comprehensively studied and fully characterized in [8]. In this brief note, we revisit these results, with a particular emphasis on the striking emergence of the golden ratio in the derived formulas.

Keywords: Local Dirichlet spaces; Taylor polynomials; Lebesgue constant (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_112

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DOI: 10.1007/978-3-032-16356-1_112

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