Interpolating sequences in the unit ball of $C^{n}$

N. Pandeski

Displaying similar documents to “Interpolating sequences in the unit ball of $C^{n}$ ”

Piatetski-Shapiro sequences via Beatty sequences

Lukas Spiegelhofer (2014)

Acta Arithmetica

Similarity:

Integer sequences of the form $⌊ n^{c} ⌋$ , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference $\sum_{n \leq x} φ (⌊ n^{c} ⌋) - 1 / c \sum_{n \leq x^{c}} φ (n) n^{1 / c - 1}$ , which measures the deviation of the mean value of φ on the subsequence $⌊ n^{c} ⌋$ from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by $⌊ n^{c} ⌋$ attains both of its values with...

Primefree shifted Lucas sequences

Lenny Jones (2015)

Acta Arithmetica

Similarity:

We say a sequence $= {(s ₙ)}_{n \geq 0}$ is primefree if |sₙ| is not prime for all n ≥ 0, and to rule out trivial situations, we require that no single prime divides all terms of . In this article, we focus on the particular Lucas sequences of the first kind, $_{a} = {(u ₙ)}_{n \geq 0}$ , defined by u₀ = 0, u₁ = 1, and uₙ = aun-1 + un-2 for n≥2, where a is a fixed integer. More precisely, we show that for any integer a, there exist infinitely many integers k such that both of the shifted sequences $_{a} \pm k$ are simultaneously primefree. This...

On linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

Similarity:

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces $H^{p} (σ)$ and the $H^{p} (σ)$ interpolating sequences S in the p-spectrum $ℳ_{p}$ of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is $H^{s} (σ)$ -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in $H^{\infty} ()$ then S is $H^{p} ()$ -interpolating with...

Discrepancy estimates for some linear generalized monomials

Roswitha Hofer, Olivier Ramaré (2016)

Acta Arithmetica

Similarity:

We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, ${([n α] β)}_{n \geq 0}$ , is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper....

On the golden number and Fibonacci type sequences

Eugeniusz Barcz (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

Similarity:

The paper presents, among others, the golden number $ϕ$ as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein’s theorem. To demonstrate the equality , where $f_{n}$ is $n$ -th Fibonacci number also the formula from Corollary has been applied. It was obtained using some relationships between Fibonacci and Lucas numbers, which were previously justified.

On square classes in generalized Fibonacci sequences

Zafer Şiar, Refik Keskin (2016)

Acta Arithmetica

Similarity:

Let P and Q be nonzero integers. The generalized Fibonacci and Lucas sequences are defined respectively as follows: U₀ = 0, U₁ = 1, V₀ = 2, V₁ = P and $U_{n + 1} = P U ₙ + Q U_{n - 1}$ , $V_{n + 1} = P V ₙ + Q V_{n - 1}$ for n ≥ 1. In this paper, when w ∈ 1,2,3,6, for all odd relatively prime values of P and Q such that P ≥ 1 and P² + 4Q > 0, we determine all n and m satisfying the equation Uₙ = wUₘx². In particular, when k|P and k > 1, we solve the equations Uₙ = kx² and Uₙ = 2kx². As a result, we determine all n such that Uₙ = 6x². ...

On the structure of sequences with forbidden zero-sum subsequences

W. D. Gao, R. Thangadurai (2003)

Colloquium Mathematicae

Similarity:

We study the structure of longest sequences in $ℤ ₙ^{d}$ which have no zero-sum subsequence of length n (or less). We prove, among other results, that for $n = 2^{a}$ and d arbitrary, or $n = 3^{a}$ and d = 3, every sequence of c(n,d)(n-1) elements in $ℤ ₙ^{d}$ which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where $c (2^{a}, d) = 2^{d}$ and $c (3^{a}, 3) = 9$ .

Equicontinuity and Convergent Sequences in the Spaces $_{C}^{'}$ and $_{M}$

Jan Kisyński (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Characterizations of equicontinuity and convergent sequences are given for the space $_{C}^{'} (ℝ ⁿ)$ of rapidly decreasing distributions and the space $_{M} (ℝ ⁿ)$ of slowly increasing infinitely differentiable functions.

Universal Jamison spaces and Jamison sequences for C₀-semigroups

Vincent Devinck (2013)

Studia Mathematica

Similarity:

An increasing sequence ${(n_{k})}_{k \geq 0}$ of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T ∈ ℬ(X) which is partially power-bounded with respect to ${(n_{k})}_{k \geq 0}$ , the set $σ_{p} (T) \cap$ is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence ${(n_{k})}_{k \geq 0}$ which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to ${(n_{k})}_{k \geq 0}$ ...

On a generalization of the Pell sequence

Jhon J. Bravo, Jose L. Herrera, Florian Luca (2021)

Mathematica Bohemica

Similarity:

The Pell sequence ${(P_{n})}_{n = 0}^{\infty}$ is the second order linear recurrence defined by $P_{n} = 2 P_{n - 1} + P_{n - 2}$ with initial conditions $P_{0} = 0$ and $P_{1} = 1$ . In this paper, we investigate a generalization of the Pell sequence called the $k$ -generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers...

On the intersection of two distinct $k$ -generalized Fibonacci sequences

Diego Marques (2012)

Mathematica Bohemica

Similarity:

Let $k \geq 2$ and define $F^{(k)} : = {(F_{n}^{(k)})}_{n \geq 0}$ , the $k$ -generalized Fibonacci sequence whose terms satisfy the recurrence relation $F_{n}^{(k)} = F_{n - 1}^{(k)} + F_{n - 2}^{(k)} + \dots + F_{n - k}^{(k)}$ , with initial conditions $0, 0, \dots, 0, 1$ ( $k$ terms) and such that the first nonzero term is $F_{1}^{(k)} = 1$ . The sequences $F : = F^{(2)}$ and $T : = F^{(3)}$ are the known Fibonacci and Tribonacci sequences, respectively. In 2005, Noe and Post made a conjecture related to the possible solutions of the Diophantine equation $F_{n}^{(k)} = F_{m}^{(ℓ)}$ . In this note, we use transcendental tools to provide a general method for finding the intersections $F^{(k)} \cap F^{(m)}$ which gives...

Multipliers of the space $A^{p}$

I. Jovanović (1986)

Matematički Vesnik

Similarity:

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

Stanisław Kwapień, Jan Mycielski (2001)

Studia Mathematica

Similarity:

The Kaczmarz algorithm of successive projections suggests the following concept. A sequence $(e_{k})$ of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and $x ₙ = x_{n - 1} + α ₙ e ₙ$ , where $α ₙ = ⟨ x - x_{n - 1}, e ₙ ⟩$ . We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.

Displaying similar documents to “Interpolating sequences in the unit ball of C n ”

Displaying similar documents to “Interpolating sequences in the unit ball of $C^{n}$ ”