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Sep 19, 2013
09/13

by
Ewa Damek; Fulvio Ricci

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Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.

Source: http://arxiv.org/abs/math/9207213v1

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Jul 20, 2013
07/13

by
Adam Korányi; Fulvio Ricci

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A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

Source: http://arxiv.org/abs/0804.1188v1

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Jun 29, 2018
06/18

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Fulvio Ricci; Amit Samanta

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Given a Lie group $G$, a compact subgroup $K$ and a representation $\tau\in\hat K$, we assume that the algebra of $\text{End}(V_\tau)$-valued, bi-$\tau$-equivariant, integrable functions on $G$ is commutative. We present the basic facts of the related spherical analysis, putting particular emphasis on the r\^ole of the algebra of $G$-invariant differential operators on the homogeneous bundle $E_\tau$ over $G/K$. In particular, we observe that, under the above assumptions, $(G,K)$ is a Gelfand...

Topics: Representation Theory, Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1604.07301

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Sep 18, 2013
09/13

by
Veronique Fischer; Fulvio Ricci

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The spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz $K$-invariant functions on $N$. We also show the converse in the case of the Gelfand pair $(SO(3)\ltimes N_{3,2}, SO(3))$, where $N_{3,2}$ is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.

Source: http://arxiv.org/abs/0809.1952v1

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Sep 24, 2013
09/13

by
Herbert Koch; Fulvio Ricci

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The twisted Laplacian in the d=2n dimensional Euclidean space has the spectrum n+2k, k a nonnegative integer. We find sharp asymptotic bounds of the norm of the projection to the eigenspace considered as map from L2 to Lp, for all p>2.

Source: http://arxiv.org/abs/math/0412236v1

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Sep 18, 2013
09/13

by
Fulvio Ricci; Joan Verdera

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In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0

Source: http://arxiv.org/abs/0809.1719v4

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Sep 21, 2013
09/13

by
Veronique Fischer; Fulvio Ricci; Oksana Yakimova

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This paper is a continuation of [8], in the direction of proving the conjecture that the spherical transform on a nilpotent Gelfand pair (N,K) establishes an isomorphism between the space of K-invariant Schwartz functions on N and the space of Schwartz functions restricted to the Gelfand spectrum properly embedded in a Euclidean space. We prove a result, of independent interest for the representation theoretical problems that are involved, which can be viewed as a generalised Hadamard lemma for...

Source: http://arxiv.org/abs/1008.4699v2

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Sep 20, 2013
09/13

by
Veronique Fischer; Fulvio Ricci; Oksana Yakimova

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The spectrum of a Gelfand pair of the form (K lx N, K), where N is a nilpotent group, can be embedded in a Euclidean space Rd . The identification of the spherical transforms of K-invariant Schwartz functions on N with the restrictions to the spectrum of Schwartz functions on Rd has been proved already when N is a Heisenberg group and in the case where N = N3,2 is the free two-step nilpotent Lie group with three generators, with K = SO3 [2, 3, 11]. We prove that the same identification holds...

Source: http://arxiv.org/abs/1002.3630v1

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Sep 22, 2013
09/13

by
Veronique Fischer; Fulvio Ricci; Oksana Yakimova

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Let (N,K) be a nilpotent Gelfand pair, i.e., N is a nilpotent Lie group, K a compact group of automorphisms of N, and the algebra D(N)^K of left-invariant and K-invariant differential operators on N is commutative. In these hypotheses, N is necessarily of step at most two. We say that (N,K) satisfies Vinberg's condition if K acts irreducibly on $n/[n,n]$, where n= Lie(N). Fixing a system D of d formally self-adjoint generators of D(N)^K, the Gelfand spectrum of the commutative convolution...

Source: http://arxiv.org/abs/1210.7962v1

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Jun 29, 2018
06/18

by
Detlef Müller; Fulvio Ricci; James Wright

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Fourier restriction theorems, whose study had been initiated by E.M. Stein, usually describe a family of a priori estimates of the L^q-norm of the restriction of the Fourier transform of a function f in L^p (say, on Euclidean space) to a given subvariety S, endowed with a suitabel measure. Such estimates allow to define the restriction Rf of the Fourier transform of an L^p-function to S in an operator theoretic sense. In this article, we begin to investigate the question what is the...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1612.04880

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Sep 21, 2013
09/13

by
Detlef Müller; Marco M. Peloso; Fulvio Ricci

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We prove that, if \Delta_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-H\"ormander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(\Delta_1) is L^p-bounded for 1

Source: http://arxiv.org/abs/math/0508543v1

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Sep 22, 2013
09/13

by
Francesca Astengo; Bianca Di Blasio; Fulvio Ricci

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Let $\Hn$ be the $(2n+1)$-dimensional Heisenberg group and $K$ a compact group of automorphisms of $\Hn$ such that $(K\ltimes \Hn,K)$ is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of $K$-invariant Schwartz functions on $\Hn$ and the space of Schwartz function on a closed subset of $\R^s$ homeomorphic to the Gelfand spectrum of the Banach algebra of $K$-invariant integrable functions on $\Hn$.

Source: http://arxiv.org/abs/0805.3809v1

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Sep 23, 2013
09/13

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Francesca Astengo; Bianca Di Blasio; Fulvio Ricci

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We prove several Paley--Wiener-type theorems related to the spherical transform on the Gelfand pair $\big(H_n\rtimes U(n),U(n)\big)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in ${\mathbb R}^2$, we prove that spherical transforms of $ U(n)$--invariant functions and distributions with compact support in $H_n$ admit unique entire extensions to ${\mathbb C}^2$, and we find real-variable characterizations...

Source: http://arxiv.org/abs/1303.0997v1

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Jun 28, 2018
06/18

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Alexander Nagel; Fulvio Ricci; Elias M. Stein; Stephen Wainger

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The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as operators that occur in sub-elliptic problems and those arising in elliptic problems. For example, one would like to describe the algebras containing the operators related to the Kohn-Laplacian for appropriate domains, or those related to inverses of...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1511.05702

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Sep 21, 2013
09/13

by
Alexander Nagel; Fulvio Ricci; Elias M. Stein; Stephen Wainger

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Let $\mathcal K$ be a flag kernel on a homogeneous nilpotent Lie group $G$. We prove that operators $T$ of the form $T(f)= f*\mathcal K$ form an algebra under composition, and that such operators are bounded on $L^{p}(G)$ for $1

Source: http://arxiv.org/abs/1108.0177v1

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Sep 23, 2013
09/13

by
Peter Raffai; Gabor Szeifert; Luca Matone; Yoichi Aso; Imre Bartos; Zsuzsa Marka; Fulvio Ricci; Szabolcs Marka

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We present an experimental opportunity for the future to measure possible violations to Newton's 1/r^2 law in the 0.1-10 meter range using Dynamic gravity Field Generators (DFG) and taking advantage of the exceptional sensitivity of modern interferometric techniques. The placement of a DFG in proximity to one of the interferometer's suspended test masses generates a change in the local gravitational field that can be measured at a high signal to noise ratio. The use of multiple DFGs in a null...

Source: http://arxiv.org/abs/1109.4258v2

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Jun 28, 2018
06/18

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Enrico Calloni; S. Caprara; Martina De Laurentis; Giampiero Esposito; M. Grilli; E. Majorana; G. P. Pepe; S. Petrarca; Paola Puppo; P. Rapagnani; Fulvio Ricci; Luigi Rosa; Carlo Rovelli; P. Ruggi; N. L. Saini; Cosimo Stornaiolo; Francesco Tafuri

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Archimedes is a feasibility study of a future experiment to ascertain the interaction of vacuum fluctuations with gravity. The experiment should measure the force that the earth's gravitational field exerts on a Casimir cavity by using a small force detector. Here we analyse the main parameters of the experiment and we present its conceptual scheme, which overcomes in principle the most critical problems.

Topics: Quantum Physics, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1511.04269