By Massimo A Picardello; Alessandro Figà-Talamanca (ed.)

This ebook illustrates the big variety of analysis matters built by means of the Italian learn team in harmonic research, initially began by means of Alessandro Figà-Talamanca, to whom it's committed within the social gathering of his retirement. specifically, it outlines a few of the extraordinary ramifications of the mathematical advancements that all started while Figà-Talamanca introduced the research of harmonic research to Italy; the examine crew that he nurtured has now elevated to hide many components. accordingly the publication is addressed not just to specialists in harmonic research, summability of Fourier sequence and singular integrals, but in addition in strength thought, symmetric areas, research and partial differential equations on Riemannian manifolds, research on graphs, bushes, constructions and discrete teams, Lie teams and Lie algebras, or even in far-reaching purposes as for example mobile automata and sign processing (low-discrepancy sampling, Gaussian noise). learn more... The Shifted Wave Equation on Damek-Ricci areas and on Homogeneous bushes / Jean-Philippe Anker, Pierre Martinot, Emmanuel Pedon -- Invariance of skill less than Quasisymmetric Maps of the Circle: a simple evidence / Nicola Arcozzi, Richard Rochberg -- A Koksma-Hlawka Inequality for Simplices / Luca Brandolini, Leonardo Colzani, Giacomo Gigante -- A twin Interpretation of the Gromov-Thurston evidence of Mostow tension and quantity stress for Representations of Hyperbolic Lattices / Michelle Bucher, Marc Burger, Alessandra Iozzi -- The Algebras Generated by means of the Laplace Operators in a Semi-homogeneous Tree / Enrico Casadio Tarabusi, Massimo A. Picardello -- Surjunctivity and Reversibility of mobile Automata over Concrete different types / Tullio Ceccherini-Silberstein, Michel Coornaert -- Pointwise Convergence of Bochner-Riesz potential in Sobolev areas / Leonardo Colzani, Sara Volpi -- Sub-Finsler Geometry and Finite Propagation pace / Michael G. Cowling, Alessio Martini -- at the Boundary habit of Holomorphic and Harmonic features / Fausto Di Biase -- developing Laplacians on restrict areas of Self-similar teams / Alfredo Donno -- a few feedback on Generalized Gaussian Noise / Saverio Giulini -- Eigenvalues of the Vertex Set Hecke Algebra of an Affine development / Anna Maria Mantero, Anna Zappa -- A Liouville kind Theorem for Carnot teams: A Case research / Alessandro Ottazzi, Ben Warhurst -- Stochastic homes of Riemannian Manifolds and purposes to PDE's / Gregorio Pacelli Bessa, Stefano Pigola, Alberto G. Setti -- Characterization of Carleson Measures for Besov areas on Homogeneous timber / Maria Rosaria Tupputi -- Atomic and Maximal Hardy areas on a Lie crew of Exponential progress / Maria Vallarino -- The Maximal Singular necessary: Estimates by way of the Singular fundamental / Joan Verdera

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A. 1007/978-88-470-2853-1_4, © Springer-Verlag Italia 2013 47 48 M. Bucher et al. The methods introduced by Mostow emphasized the role of the quasi-isometries of Mi = Hn , their quasi-conformal extension to ∂Hn , ergodicity phenomena of the Γi -action on ∂Hn , as well as almost everywhere differentiability results à la Egorov. In the 1970’s, a new approach for rigidity in the real hyperbolic case was developed by Gromov. In this context he introduced 1 -homology and the simplicial volume: techniques like smearing and straightening became important.

Random walks on a tree and capacity in the interval. Ann. Inst. Henri Poincaré Probab. Stat. 28, 557–592 (1992) 5. : The boundary correspondence under quasiconformal mappings. Acta Math. 96, 125–142 (1956) 6. : Teichmüller theory and the universal period mapping via quantum calculus and the H 1/2 space on the circle. Osaka J. Math. 32, 1–34 (1995) A Koksma–Hlawka Inequality for Simplices Luca Brandolini, Leonardo Colzani, Giacomo Gigante, and Giancarlo Travaglini Abstract We estimate the error in the approximation of the integral of a smooth function over a parallelepiped Ω or a simplex S by Riemann sums with deterministic Zd -periodic nodes.

Ggq ) endowed with its usual homogeneous coboundary operator δ : Cc Gq+1 , R(ε) G → Cc Gq+2 , R(ε) G defined by q+1 δf (g0 , . . , gq+1 ) := (−1)j f (g0 , . . , gj −1 , gj +1 , . . , gq+1 ). ,gq ∈G G f (g0 , . . , gq ) < +∞ q and the continuous bounded cohomology Hc,b (G, R(ε) ) of G with coefficients in R(ε) is the cohomology of this cocomplex. The inclusion Cc,b Gq+1 , R(ε) G ⊂ Cc Gq+1 , R(ε) G induces a comparison map q q c : Hc,b (G, R(ε) ) −→ Hc (G, R(ε) ). We call cochains in Cc,(b) (Gq+1 , R)G invariant and cochains in Cc,(b) (Gq+1 , Rε )G equivariant and apply this terminology to the cohomology classes as well.