Abstract The Fourier and Fourier–Stieltjes algebras over locally compact groupoids have been defined in a way that parallels their construction for groups. In this article, we extend the results on surjectivity or lack of restriction map groups to groupoid setting. particular, consider maps restrict domain these functions algebra an isotropy subgroup. These are continuous contractive homomorphisms. When is étale, show surjective. not surjective general. We prove transitive with section group...

This paper proves that if $G$ is a graph (parallel edges allowed) of maximum degree 3, then $χ_c'(G) \leq 11/3$ provided does not contain $H_1$ or $H_2$ as subgraph, where and are obtained by subdividing one edge $K_2^3$ (the with three parallel between two vertices) $K_4$, respectively. As $χ_c'(H_1) = χ_c'(H_2) 4$, our result implies there no $11/3 < χ_c'(G) 4$. It also 2-edge connected cubic graph, $χ'(G) \le 11/3$.

Rajchman measures of locally compact Abelian groups are studied for almost a century now, and they play an important role in the study trigonometric series.Eymard's influential work allowed generalizing these to case non-Abelian G.The algebra G, which we denote by B 0 (G), is set all elements Fourier-Stieltjes that vanish at infinity.In present article, characterize have amenable algebras.We show (G) if only G Abelian.On other extreme, many examples groups, such as non-compact infinite...

Abstract This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′ c ( ) ≤ 11/3 provided does not contain H 1 or 2 as subgraph, where and are obtained by subdividing one edge K (the with three parallel between two vertices) 4 , respectively. As = 4, our result implies there no < 4. It also 2‐edge connected cubic graph, 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335,

Let<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding="application/x-tex">G</mml:annotation></mml:semantics></mml:math></inline-formula>be a compact connected Lie group. The question of when weighted Fourier algebra on<inline-formula encoding="application/x-tex">G</mml:annotation></mml:semantics></mml:math></inline-formula>is completely isomorphic to an operator will...

The emerging field of graph signal processing aims to develop analysis and techniques for data that is best represented on irregular domains such as graphs. To this end, important notions classical processing, smoothness, band-limitedness, sampling, should be extended the case signals. One most fundamental concepts in Fourier transform. Recently, transform was defined a generalization Abelian groups, many its properties were investigated. However, usually manifestation non-commutative...

A square symmetric matrix is a Robinson similarity if entries in its rows and columns are nondecreasing when moving toward the diagonal. can be viewed as affinity between objects arranged linear order, where closer together have higher affinity. We define new parameter, $\Gamma_{1}$, which measures how badly given fails to similarity. Namely, precisely $\Gamma_{1}$ attains zero, with small close (in normalized $\ell^1$-norm) matrix. Moreover, both approximation computed polynomial time....

We consider the problem of characterizing Sobolev wavefront set a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms its continuous wavelet transform, with latter being defined respect to suitably chosen dilation group $H\subset{\rm GL}(\mathbb{R}^{d})$. derive necessary and sufficient criteria for elements set, formulated decay behaviour given generalized transform. It turns out that characterization directed smoothness finite order can be performed two important cases: (1)...

We consider a recently proposed approach to graph signal processing based on graphons. show how the graphon-based GSP applies graphs sampled from stochastic block model. obtain basis for graphon Fourier transform such samples directly link probability matrix and sizes of This formulation allows us bound sensitivity small changes in sizes. then focus case where corresponds (weighted) Cayley graph. If are equal, nice can be derived underlying group. explore how, not some or all properties...