Widths of a Class of Analytic Functions

Parfenov, O. G.

doi:10.1070/sm1983v045n02abeh002600

Cited by 12 publications

(5 citation statements)

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“…It is believed Parfenov and Fomin report that the base-catalyzed exchange reaction of S-arenesulfenamides with S-esters of thiocarboxylic acids yields amides and disulfides (eq 43). 33 The reaction does not proceed in the absence of a catalytic amount of a trivalent phosphorus compound. The authors suggest the following mechanism for this reaction (eq 44): Similar phosphorus(III)-catalyzed reactions of sulfenamides with linear anhydrides (eq 45) and carboxylic acid chlorides (eq 46) yield the indicated amides.…”

Section: A Reactions With Electrophilesmentioning

confidence: 99%

The chemistry of sulfenamides

Craine¹,

Raban²

1989

Chem. Rev.

213

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Section: A Reactions With Electrophilesmentioning

confidence: 99%

The chemistry of sulfenamides

Craine¹,

Raban²

1989

Chem. Rev.

213

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“…)1.2 is positive and continuous on Tr; in accordance with the lemma on approximation of continuous weights by Blaschke products (see [2]), there exists a sequence of Blaschke products {B,,}~ ~ such that…”

Section: J0 __+mentioning

confidence: 65%

“…In [2], the following asymptotic formula was proved for the singular numbers of j0 (where u is an arbitrary measure with G(u) # 0):…”

Section: J0 __+mentioning

confidence: 99%

Bernstein and Gelfand widths of certain classes of analytic functions. II

Parfenov¹

1998

J Math Sci

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The Gelfand widths of the unit ball of H2(v) We emphasize that no conditions are imposed on v, except G(v) # 0 and the condition of finiteness. If G(v) = 0, then the order of decay of the sequence {d"(Ja)} changes. Now, let tt be an arbitrary finite Borel measure on T~, and let G(#) be the geometric mean of t* with respect to the normalized Lebesgue measure on T~. We consider the embedding operator Thus, this paper is aimed at lifting all irrelevant conditions on the measure. In passing, we discuss a Bernstein-type inequality for polynomials and for certain spaces of rational functions. At the end, we discuss the limit case in Theorem 2, namely, the embedding J : H ~ --+ L~(T, #). Proof of Theorem t.Though the lower estimate is an easy consequence of the results of [1], we recall its proof for the sake of Completeness. We introduce the embedding operator *We recall that G(v) = exp(f tn(dv/dm)drn). T j0 __+

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“…Moreover, (3.11) holds under much weaker assumptions. [32], [38]). Finally, we mention the following corollary of (3.7) which is of independent interest (cf.…”

Section: It Follows From (33) Thatmentioning

confidence: 99%

Best Meromorphic Approximation of Markov Functions on the Unit Circle

Baratchart¹,

Prokhorov²,

Saff³

2001

Found. Comput. Math.

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Let E ⊂ (−1, 1) be a compact set, let µ be a positive Borel measure with support supp µ = E, and let H p (G), 1 ≤ p ≤ ∞, be the Hardy space of analytic functions on the open unit disk G with circumference = {z: |z| = 1}. Let n, p be the error in best approximation of the Markov functionin the space L p ( ) by meromorphic functions that can be represented in the form h = P/Q, where P ∈ H p (G), Q is a polynomial of degree at most n, Q ≡ 0. We investigate the rate of decrease of n, p , 1 ≤ p ≤ ∞, and its connection with n-widths. The convergence of the best meromorphic approximants and the limiting Date distribution of poles of the best approximants are described in the case when 1 < p ≤ ∞ and the measure µ with support E = [a, b] satisfies the Szegő condition b a log(dµ/dx)

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Widths of a Class of Analytic Functions

Cited by 12 publications

References 1 publication

The chemistry of sulfenamides

The chemistry of sulfenamides

Bernstein and Gelfand widths of certain classes of analytic functions. II

Best Meromorphic Approximation of Markov Functions on the Unit Circle

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