Transferring $L^{p}$ eigenfunction bounds from $S^{2n+1}$ to hⁿ

Valentina Casarino; Paolo Ciatti

Displaying similar documents to “Transferring $L^{p}$ eigenfunction bounds from $S^{2 n + 1}$ to hⁿ”

$H^{\infty}$ calculus and dilatations

Andreas M. Fröhlich, Lutz Weis (2006)

Bulletin de la Société Mathématique de France

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We characterise the boundedness of the $H^{\infty}$ calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if $- A$ generates a bounded analytic $C_{0}$ semigroup $(T_{t})$ on a UMD space, then the $H^{\infty}$ calculus of $A$ is bounded if and only if $(T_{t})$ has a dilation to a bounded group on $L^{2} ([0, 1], X)$ . This generalises a Hilbert space result of C.LeMerdy. If $X$ is an $L^{p}$ space we can choose another $L^{p}$ space in place of $L^{2} ([0, 1], X)$ .

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

Centralizing traces and Lie-type isomorphisms on generalized matrix algebras: a new perspective

Xinfeng Liang, Feng Wei, Ajda Fošner (2019)

Czechoslovak Mathematical Journal

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Let $ℛ$ be a commutative ring, $𝒢$ be a generalized matrix algebra over $ℛ$ with weakly loyal bimodule and $𝒵 (𝒢)$ be the center of $𝒢$ . Suppose that $𝔮 : 𝒢 \times 𝒢 \to 𝒢$ is an $ℛ$ -bilinear mapping and that $𝔗_{𝔮} : 𝒢 \to 𝒢$ is a trace of $𝔮$ . The aim of this article is to describe the form of $𝔗_{𝔮}$ satisfying the centralizing condition $[𝔗_{𝔮} (x), x] \in 𝒵 (𝒢)$ (and commuting condition $[𝔗_{𝔮} (x), x] = 0$ ) for all $x \in 𝒢$ . More precisely, we will revisit the question of when the centralizing trace (and commuting trace) $𝔗_{𝔮}$ has the so-called proper form from a new perspective. Using the aforementioned...

The unit groups of semisimple group algebras of some non-metabelian groups of order $144$

Gaurav Mittal, Rajendra K. Sharma (2023)

Mathematica Bohemica

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We consider all the non-metabelian groups $G$ of order $144$ that have exponent either $36$ or $72$ and deduce the unit group $U (𝔽_{q} G)$ of semisimple group algebra $𝔽_{q} G$ . Here, $q$ denotes the power of a prime, i.e., $q = p^{r}$ for $p$ prime and a positive integer $r$ . Up to isomorphism, there are $6$ groups of order $144$ that have exponent either $36$ or $72$ . Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order $144$ that are a direct product of two...

An application of the method wherein the $p h i$ - and $c h i$ - methods are combined for the determination of the grating constant. [II.]

Swami Jnanananda (1936)

Časopis pro pěstování matematiky a fysiky

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The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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On C $^{*}$ -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

Annales Polonici Mathematici

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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On the $p^{λ}$ problem

Stephan Baier (2004)

Acta Arithmetica

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On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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Геометрическая теория состояний, граница фон Неймана, двойственность $C^{*}$ -алгерб

А.М. Вершик (1972)

Zapiski naucnych seminarov Leningradskogo

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On the equation $ϕ (x + m) = ϕ (x) + m$

A. Makowski (1964)

Matematički Vesnik

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Localization techniques in $L^{p}$ spaces

A. Pełczyński, H. Rosenthal (1975)

Studia Mathematica

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The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

Matematički Vesnik

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On spirallike functions of order $α$ and type $β$ with fixed second coefficient

M. K. Aouf (1988)

Matematički Vesnik

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Inequalities for real number sequences with applications in spectral graph theory

Emina Milovanović, Şerife Burcu Bozkurt Altındağ, Marjan Matejić, Igor Milovanović (2022)

Czechoslovak Mathematical Journal

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Let $a = (a_{1}, a_{2}, ..., a_{n})$ be a nonincreasing sequence of positive real numbers. Denote by $S = {1, 2, ..., n}$ the index set and by $J_{k} = {I = {r_{1}, r_{2}, ..., r_{k}}$ , $1 \leq r_{1} < r_{2} < \dots < r_{k} \leq n}$ the set of all subsets of $S$ of cardinality $k$ , $1 \leq k \leq n - 1$ . In addition, denote by $a_{I} = a_{r_{1}} + a_{r_{2}} + \dots + a_{r_{k}}$ , $1 \leq k \leq n - 1$ , $1 \leq r_{1} < r_{2} < \dots < r_{k} \leq n$ , the sum of $k$ arbitrary elements of sequence $a$ , where $a_{I_{1}} = a_{1} + a_{2} + \dots + a_{k}$ and $a_{I_{n}} = a_{n - k + 1} + a_{n - k + 2} + \dots + a_{n}$ . We consider bounds of the quantities $R S_{k} (a) = a_{I_{1}} / a_{I_{n}}$ , $L S_{k} (a) = a_{I_{1}} - a_{I_{n}}$ and $S_{k, α} (a) = \sum_{I \in J_{k}} a_{I}^{α}$ in terms of $A = \sum_{i = 1}^{n} a_{i}$ and $B = \sum_{i = 1}^{n} a_{i}^{2}$ . Then we use the obtained results to generalize some results regarding Laplacian and normalized Laplacian eigenvalues of graphs.

On open maps and related functions over the Salbany compactification

Mbekezeli Nxumalo (2024)

Archivum Mathematicum

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Given a topological space $X$ , let $𝒰 X$ and $η_{X} : X \to 𝒰 X$ denote, respectively, the Salbany compactification of $X$ and the compactification map called the Salbany map of $X$ . For every continuous function $f : X \to Y$ , there is a continuous function $𝒰 f : 𝒰 X \to 𝒰 Y$ , called the Salbany lift of $f$ , satisfying $(𝒰 f) \circ η_{X} = η_{Y} \circ f$ . If a continuous function $f : X \to Y$ has a stably compact codomain $Y$ , then there is a Salbany extension $F : 𝒰 X \to Y$ of $f$ , not necessarily unique, such that $F \circ η_{X} = f$ . In this paper, we give a condition on a space such that its Salbany map is open. In...

Displaying similar documents to “Transferring L p eigenfunction bounds from S 2 n + 1 to hⁿ”

Displaying similar documents to “Transferring $L^{p}$ eigenfunction bounds from $S^{2 n + 1}$ to hⁿ”