Operator theorems on $L^P$-convergence to zero $(1 \leqslant p &lt; + \infty )$

R. Zaharopol

Displaying similar documents to “Operator theorems on $L^{P}$ -convergence to zero $(1 ⩽ p < + \infty)$ ”

Sets of parts such that the partition function is even

Ben Saïd, J.-N. Nicolas (2003)

Acta Arithmetica

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On the partition of the genotypic function

W. Klonecki (1966)

Applicationes Mathematicae

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An application of Pólya’s enumeration theorem to partitions of subsets of positive integers

Xiao Jun Wu, Chong-Yun Chao (2005)

Czechoslovak Mathematical Journal

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Let $S$ be a non-empty subset of positive integers. A partition of a positive integer $n$ into $S$ is a finite nondecreasing sequence of positive integers $a_{1}, a_{2}, \dots, a_{r}$ in $S$ with repetitions allowed such that $\sum_{i = 1}^{r} a_{i} = n$ . Here we apply Pólya’s enumeration theorem to find the number $¶ (n; S)$ of partitions of $n$ into $S$ , and the number $D P (n; S)$ of distinct partitions of $n$ into $S$ . We also present recursive formulas for computing $¶ (n; S)$ and $D P (n; S)$ .

A combinatorial proof of Andrews' smallest parts partition function.

Ji, Kathy Qing (2008)

The Electronic Journal of Combinatorics [electronic only]

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On some general problems in the theory of partitions, I

P Erdös, P. Turán (1971)

Acta Arithmetica

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On a certain analogy of Stirling's numbers of the 2nd kind

Robert Karpe (1973)

Archivum Mathematicum

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On a conjecture of Andrews.

Padmavathamma, Sudha, T.G. (1993)

International Journal of Mathematics and Mathematical Sciences

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Parity indices of partitions

Kağan Kurşungöz (2010)

Acta Arithmetica

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Generalized interval exchanges and the 2–3 conjecture

Shmuel Friedland, Benjamin Weiss (2005)

Open Mathematics

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We introduce the notion of a generalized interval exchange $φ_{𝒜}$ induced by a measurable k-partition $𝒜 = \{A_{1}, . . ., A_{k}\}$ of [0,1). $φ_{𝒜}$ can be viewed as the corresponding restriction of a nondecreasing function $f_{𝒜}$ on ℝ with $f_{𝒜} (0) = 0, f_{𝒜} (k) = 1$ . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that $f_{𝒜} \circ f_{ℬ} = f_{ℬ} \circ f_{𝒜}$ . We give necessary and sufficient conditions for this equality to hold. We...

Displaying similar documents to “Operator theorems on L P -convergence to zero ( 1 ⩽ p &lt; + ∞ ) ”

Displaying similar documents to “Operator theorems on $L^{P}$ -convergence to zero $(1 ⩽ p < + \infty)$ ”