Canadian Journal of Mathematics
Multilinear transference of Fourier and Schur multipliers acting on noncommutative $L_p$-spaces
Let G be a locally compact unimodular group, and let be some function of n variables on G. To such a , one can associate a multilinear Fourier multiplier, which acts on some n-fold product of the noncommutative -spaces of the group von Neumann algebra…
Canadian Journal of Mathematics
Abel universal functions
Given a sequence tending to , we consider the set of Abel universal functions consisting of holomorphic functions f in the open unit disk such that for any compact set K included in the unit circle , different from , the set is dense in the space …
Canadian Journal of Mathematics
Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set
We apply capacities to explore the space–time fractional dissipative equation: (0.1)where and . In this paper, we focus on the regularity and the blow-up set of mild solutions to (0.1). First, we establish the Strichartz-type estimates for the homogen…
Canadian Journal of Mathematics
Percolation probability and critical exponents for site percolation on the UIPT
We derive three critical exponents for Bernoulli site percolation on the uniform infinite planar triangulation (UIPT). First, we compute explicitly the probability that the root cluster is infinite. As a consequence, we show that the off-critical expon…
Canadian Journal of Mathematics
The Cuntz semigroup of unital commutative AI-algebras
We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form for some -space X. In our investigations, we also uncover new properties that th…
Canadian Journal of Mathematics
Two general series identities involving modified Bessel functions and a class of arithmetical functions
We consider two sequences and , , generated by Dirichlet series satisfying a familiar functional equation involving the gamma function . Two general identities are established. The first involves the modified Bessel function , and can be thought of as…
Canadian Journal of Mathematics
Reconstruction problems of convex bodies from surface area measures and lightness functions
First, we build a computational procedure to reconstruct the convex body from a pre-given surface area measure. Nontrivially, we prove the convergence of this procedure. Then, the sufficient and necessary conditions of a Sobolev binary function to be a…
Canadian Journal of Mathematics
Spectra of infinite graphs via freeness with amalgamation
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs, we derive a new variational formula for the spe…