scholarly journals Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

2001 ◽  
Vol 26 (3) ◽  
pp. 129-160 ◽  
Author(s):  
Victor Nistor
Keyword(s):  
Hecke Algebras ◽  
Hochschild Homology ◽  
Cyclic Homology ◽  
Detailed Calculation ◽  
Orbital Integrals ◽  
Compactly Supported ◽  
Shalika Germs ◽  
Definition Of ◽  
Compactly Supported Functions

We give a detailed calculation of the Hochschild and cyclic homology of the algebra𝒞c∞(G)of locally constant, compactly supported functions on a reductivep-adic groupG. We use these calculations to extend to arbitrary elements the definition of the higher orbital integrals introduced by Blanc and Brylinski (1992) for regular semi-simple elements. Then we extend to higher orbital integrals some results of Shalika (1972). We also investigate the effect of the “induction morphism” on Hochschild homology.

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

scholarly journals Pro unitality and pro excision in algebraic K-theory and cyclic homology

2018 ◽  
Vol 2018 (736) ◽  
pp. 95-139 ◽  
Author(s):  
Matthew Morrow
Keyword(s):  
Short Proof ◽  
Hochschild Homology ◽  
Cyclic Homology ◽  
Strong Form ◽  
Noetherian Rings ◽  
General Base ◽  
Continuity Properties ◽  
Suitable Sense ◽  
K Theory

AbstractThe purpose of this paper is to study pro excision in algebraicK-theory and cyclic homology, after Suslin–Wodzicki, Cuntz–Quillen, Cortiñas, and Geisser–Hesselholt, as well as continuity properties of André–Quillen and Hochschild homology. A key tool is first to establish the equivalence of various pro Tor vanishing conditions which appear in the literature.This allows us to prove that all ideals of commutative, Noetherian rings are pro unital in a suitable sense. We show moreover that such pro unital ideals satisfy pro excision in derived Hochschild and cyclic homology. It follows hence, and from the Suslin–Wodzicki criterion, that ideals of commutative, Noetherian rings satisfy pro excision in derived Hochschild and cyclic homology, and in algebraicK-theory.In addition, our techniques yield a strong form of the pro Hochschild–Kostant–Rosenberg theorem; an extension to general base rings of the Cuntz–Quillen excision theorem in periodic cyclic homology; a generalisation of the Feĭgin–Tsygan theorem; a short proof of pro excision in topological Hochschild and cyclic homology; and new Artin–Rees and continuity statements in André–Quillen and Hochschild homology.

Study of High Dimensional Orthogonal Vector-Valued Wavelet with Scale 4

2013 ◽  
Vol 790 ◽  
pp. 665-668
Author(s):  
Wei Qing Yang
Keyword(s):  
Multiresolution Analysis ◽  
High Dimensional ◽  
Orthogonal Vector ◽  
Compactly Supported ◽  
Definition Of ◽  
Vector Valued

In this paper, we introduce the definition of vector-valued multiresolution analysis with scale 4 and orthogonal vector-valued wavelet with scale 4 is gived. The properties of compactly supported orthogonal vector-valued wavelets with scale 4 are proved.

scholarly journals Relation between two twisted inverse image pseudofunctors in duality theory

2014 ◽  
Vol 151 (4) ◽  
pp. 735-764 ◽  
Author(s):  
Srikanth B. Iyengar ◽  
Joseph Lipman ◽  
Amnon Neeman
Keyword(s):  
Finite Type ◽  
Duality Theory ◽  
Inverse Image ◽  
Base Change ◽  
Hochschild Homology ◽  
Fundamental Class ◽  
Compactly Supported ◽  
Canonical Map ◽  
Flat Base ◽  
Derived Functors

Grothendieck duality theory assigns to essentially finite-type maps $f$ of noetherian schemes a pseudofunctor $f^{\times }$ right-adjoint to $\mathsf{R}f_{\ast }$, and a pseudofunctor $f^{!}$ agreeing with $f^{\times }$ when $f$ is proper, but equal to the usual inverse image $f^{\ast }$ when $f$ is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken to an isomorphism by ‘compactly supported’ versions of standard derived functors. Concrete realizations are described, for instance for maps of affine schemes. Applications include proofs of reduction theorems for Hochschild homology and cohomology, and of a remarkable formula for the fundamental class of a flat map of affine schemes.

scholarly journals Fourier transforms of powers of well-behaved 2D real analytic functions

2018 ◽  
Vol 30 (3) ◽  
pp. 723-732
Author(s):  
Michael Greenblatt
Keyword(s):  
Analytic Functions ◽  
Fourier Transforms ◽  
Newton Polygon ◽  
Companion Paper ◽  
Two Dimensional ◽  
Compactly Supported ◽  
Sharp Estimates ◽  
Real Analytic Functions ◽  
Real Analytic ◽  
Compactly Supported Functions

AbstractThis paper is a companion paper to [6], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [6] are stated in a rather general form. In this paper, we expand on the results of [6] and show that there is a class of “well-behaved” functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.

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