Authors:Kathryn E. Hare; Jimmy He Abstract: Let G be a compact, connected simple Lie group and \(\mathfrak {g}\) its Lie algebra. It is known that if \(\mu \) is any G-invariant measure supported on an adjoint orbit in \(\mathfrak {g}\) , then for each integer k, the k-fold convolution product of \(\mu \) with itself is either singular or in \( L^{2}\) . This was originally proven by computations that depended on the Lie type of \(\mathfrak {g}\) , as well as properties of the measure. In this note, we observe that the validity of this dichotomy is a direct consequence of the Duistermaat–Heckman theorem from symplectic geometry and that, in fact, any convolution product of (even distinct) orbital measures is either singular or in \(L^{2+\varepsilon }\) for some \(\varepsilon >0\) . An abstract transference result is given to show that the \(L^{2}\) -singular dichotomy holds for certain of the G-invariant measures supported on conjugacy classes in G. PubDate: 2018-01-11 DOI: 10.1007/s40574-017-0154-9

Authors:Maurizio Brunetti; Adriana Ciampella Abstract: Abstract Let p be an odd prime. In this paper we determine the group of length-preserving automorphisms for the ordinary Steenrod algebra A(p) and for \({\mathcal {B}}(p)\) , the algebra of cohomology operations for the cohomology of cocommutative \(\mathbb {F}_p\) -Hopf algebras. Contrarily to the \(p=2\) case, no length-preserving strict monomorphism turns out to exist. PubDate: 2018-01-10 DOI: 10.1007/s40574-017-0155-8

Authors:Francesco Bastianelli Abstract: Abstract The purpose of this note is to fix an imprecision in Theorem 3.3 of the original paper, which affects the correctness of the statement and leads to a mistake PubDate: 2018-01-08 DOI: 10.1007/s40574-017-0153-x

Authors:Qi Han Pages: 503 - 515 Abstract: Abstract In this paper, we describe a family of meromorphic functions in \(\mathbf {C}\) from analyzing some properties of these L-functions in the extended Selberg class and show two uniqueness results of such a function, in terms of shared values with a general meromorphic function in \(\mathbf {C}\) . In particular, we show the condition “ \(\displaystyle {1\mathsf{CM}+3\mathsf{IM}}\) value-sharing” suffices. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0081-1 Issue No:Vol. 10, No. 4 (2017)

Authors:Heybetkulu Mustafayev; Novruz Bashirov Pages: 517 - 527 Abstract: Abstract In this paper, some results concerning spectral properties of multipliers on commutative semisimple Banach algebras are obtained. The study concentrates on multipliers on uniformly regular Banach algebras whose Helgason–Wang representation vanish at infinity. A spectral mapping theorem for convolution operators induced by representations of locally compact abelian groups is also given. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0082-0 Issue No:Vol. 10, No. 4 (2017)

Authors:Sushanta Kumar Mohanta Pages: 529 - 548 Abstract: Abstract The purpose of this paper is to obtain sufficient conditions for the existence and uniqueness of points of coincidence and common fixed points for mappings defined on cone modular spaces endowed with a graph. Our results will improve and supplement several recent results in the literature. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0086-9 Issue No:Vol. 10, No. 4 (2017)

Authors:R. P. Pakshirajan Pages: 575 - 584 Abstract: Abstract Let x be a standard Wiener process on \([0,\ 1]\) , starting at the origin and with all its sample functions lying in the H \(\ddot{\text {o}}\) lder space \(H_{\alpha }^0\) of exponent \(\alpha ,\ 0< \alpha < \frac{1}{2}\) . Define for \(n = 1, 2, \ldots \) processes \(x_n\) and \(z_n :\ x_n(t) = \frac{x(nt)}{\sqrt{n}}\) and \(z_n(t) = \frac{x(nt)}{\sqrt{n}f(n)},\ t \in [0,\ 1]\) where \(f(n) \rightarrow \infty \) and \(\frac{f(n)}{\sqrt{\log \log n}} \rightarrow 0\) . In this paper, we show that the limit set of each of the random sequences \((x_n)\) and ( \(z_n\) ) of elements in \(H_{\alpha }^0\) in its norm topology is all of the space \(H_{\alpha }^0\) . PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0089-6 Issue No:Vol. 10, No. 4 (2017)

Authors:T. S. S. R. K. Rao Pages: 585 - 589 Abstract: Abstract In this paper we exhibit new classes of Banach spaces for which strong notions of optimization can be lifted from quotient spaces. Motivated by a well known result of Cheney and Wulbert on lifting of proximinality from a quotient space to a subspace, for closed subspaces, \(Z \subset Y \subset X\) , we consider stronger forms of optimization, that Z has in X and the quotient space Y / Z has in X / Z should lead to the conclusion Y has the same property in X. The versions we consider have been studied under various names in the literature as L-proximinal subspaces or subspaces that have the strong- \(1\frac{1}{2}\) -ball property. We give an example where the strong- \(1\frac{1}{2}\) -ball property fails to lift to the quotient. We show that if every M-ideal in Y is a M-summand, for a finite codimensional subspace \(Z \subset Y\) , that is a M-ideal in X with the strong- \(1\frac{1}{2}\) -ball property in X and if Y / Z has the \(1\frac{1}{2}\) -ball property in X / Z, then Y has the strong- \(1\frac{1}{2}\) -ball property in X. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0090-0 Issue No:Vol. 10, No. 4 (2017)

Authors:Patricia Couto G. Mauro; Dinamérico P. Pombo Pages: 591 - 594 Abstract: Abstract For any discrete valuation ring R, any R-linear mapping u from an R-module E into an R-module F and any \(y_0\in F\) , a necessary and sufficient condition for the solvability of the equation \(u(x)=y_0\) is established, and an application of this result is presented. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0096-7 Issue No:Vol. 10, No. 4 (2017)

Authors:Kamal Paykan Pages: 607 - 616 Abstract: Abstract A ring is quasi-Baer (respectively, right p.q.-Baer) in case the right annihilator of every (respectively, principal right) ideal is generated by an idempotent, as a right ideal. A ring R is right AIP if the right annihilator of any right ideal of R is pure as a right ideal. In this article, we study relations between the quasi-Baer, right p.q.-Baer, and right AIP properties of a ring R, and its skew Hurwitz series ring \((HR, \alpha )\) , where R is a ring equipped with an endomorphism \(\alpha \) . Examples to illustrate and delimit the theory are provided. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0098-5 Issue No:Vol. 10, No. 4 (2017)

Authors:L. Boccardo; F. Murat Pages: 617 - 625 Abstract: Abstract We consider a nonlinear equation with a monotone operator acting in \(W^{1, p}_0 (\Omega )\) , a lower order term \(u u ^{n-1}\) , and a source term in \(L^m (\Omega )\) with a poor summability \(m > 1\) or even \(m = 1\) . When the power n increases and tends to \(\infty \) , we prove that the (conveniently defined) solution of this problem converges (in a convenient sense) to the solution of the variational inequality posed on the convex set \(\{ v \in W^{1, p}_0(\Omega ) : v(x) \le 1 \}\) . PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0093-x Issue No:Vol. 10, No. 4 (2017)

Authors:Zhanmin Zhu Pages: 627 - 636 Abstract: Abstract A ring R is called right WP-injective if for any \(0\ne a\in R\) , there exist \(b\in R\) such that \(ab=ba\ne 0\) and any right R-homomorphism from abR to R extends to an endomorphism of R. A series of conditions under which right WP-injective rings are quasi-Frobenius rings are given, some results improve known results on quasi-Frobenius rings. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0104-y Issue No:Vol. 10, No. 4 (2017)

Authors:Raj Kumar; Ashok K. Sah Pages: 637 - 647 Abstract: Abstract In this paper we study stability of multivariate wave packet frames. Necessary and sufficient conditions for a certain system to be multivariate wave packet frames are obtained. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0106-9 Issue No:Vol. 10, No. 4 (2017)

Authors:Michael Axtell; Nicholas R. Baeth; Joe Stickles Pages: 649 - 670 Abstract: Abstract The self-idealization of a commutative ring R is isomorphic to the ring \(R[x]/(x^2)\) or, equivalently, the ring of upper-triangular Toeplitz matrices \({{\mathrm{\mathcal {T}}}}(R)=\left\{ \left( \begin{matrix} a &{} b \\ 0 &{} a \end{matrix}\right) :a,b\in R\right\} \) . Recently, Chang and Smertnig characterized the sets of lengths of factorizations in \({{\mathrm{\mathcal {T}}}}(D)\) where D is a principal ideal domain. In this work, in addition to correcting an error in their paper, we extend the study to \({{\mathrm{\mathcal {T}}}}(R)\) when R is either a principal ideal ring or a unique factorization ring. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0107-8 Issue No:Vol. 10, No. 4 (2017)

Authors:Hawete Hattab Pages: 671 - 679 Abstract: Abstract Let (G, X) be a flow such that X is a locally finite graph and G is a finitely generated group. In this paper, it is shown that the following properties are equivalent: (G, X) is pointwise recurrent; (G, X) is pointwise periodic; (G, X) is pointwise almost periodic. We show that every pointwise recurrent flow of a locally finite graph is equicontinuous. We also give some qualitative properties of an equicontinuous flow. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0109-6 Issue No:Vol. 10, No. 4 (2017)

Authors:A. M. Mantero; A. Zappa Pages: 681 - 724 Abstract: Abstract Let \({\Delta }\) be an affine building of type \(\widetilde{A}_2\) and \({\Omega }\) its maximal boundary. We prove that, for every function \(f \in L^1({\Omega }),\) restricted convergence of the normalized generalized Poisson transform \({\mathcal {P}}_{{\chi }} f / {\mathcal {P}}_{{\chi }} 1\) to f holds almost everywhere. PubDate: 2017-12-01 DOI: 10.1007/s40574-016-0110-0 Issue No:Vol. 10, No. 4 (2017)

Authors:Rasoul Akrami; Ali Reza Janfada; Mohammad Reza Miri Abstract: Abstract Let \(\mathcal {M}\) be a Hilbert \(C^*\) -module. Set \( x =\big <x,x\big >^\frac{1}{2}\) for every \(x\in \mathcal {M}\) and \(\mathcal {C}=\overline{\{\big <x,y\big >:x,y\in \mathcal {M}\}}\) . We prove that \( xa = x a \) for every \(x\in \mathcal {M}\) and \(a\in \mathcal {C}\) if and only if \(\mathcal {C}\) is a commutative \(C^*\) -algebra. PubDate: 2017-12-26 DOI: 10.1007/s40574-017-0152-y

Authors:Omran Kouba Abstract: Abstract Consider a sequence \((a_n)_{n\ge 1}\) of complex numbers such that for some positive number p we have \(\lim _{n\rightarrow \infty }\frac{1}{n^p}\left( \sum _{k=1}^na_k\right) =\ell \in \mathbb {C}\) . We prove that, under some mild conditions on the sequence (positivity or absolute boundedness in the mean, etc.), we have $$\begin{aligned} \lim _{n\rightarrow \infty } \frac{1}{n^{q}}\sum _{k=1}^nk^{q-p}a_kf\left( \frac{k}{n}\right) = p\ell \int _0^1x^{q-1}f(x)dx \end{aligned}$$ for all \(q>0\) and all Riemann integrable functions \(f:[0,1]\rightarrow \mathbb {C}\) . Some applications to probability theory and to number theory are also discussed. PubDate: 2017-12-20 DOI: 10.1007/s40574-017-0151-z

Authors:Giovanni Cimatti Abstract: Abstract A theorem on the solutions of the problem \(U'(w)={\gamma }F(U(w),w), U(w_1)=u_1,\ U(w_2)=u_2\) is applied for finding the functional solutions of the system of partial differential equations $$\begin{aligned} {\nabla }\cdot (a(u,w){\nabla }u)= & {} 0,\quad u=u_1{\ \hbox {on}\quad {{\Gamma }}_1},\quad u=u_2{\ \hbox {on}\quad {{\Gamma }}_2},\quad \frac{{\partial }u}{{\partial }n}=0{\ \hbox {on}\quad {{\Gamma }}_3} \\ {\nabla }\cdot (b(u,w){\nabla }w)= & {} 0,\quad w=w_1{\ \hbox {on}\quad {{\Gamma }}_1},\quad w=w_2{\ \hbox {on}\quad {{\Gamma }}_2},\quad \frac{{\partial }w}{{\partial }n}=0{\ \hbox {on}\quad {{\Gamma }}_3}. \end{aligned}$$ The problem of existence and uniqueness of solutions is considered. PubDate: 2017-12-12 DOI: 10.1007/s40574-017-0150-0

Authors:Matteo Casati; Daniele Valeri Abstract: Abstract We give an introduction to the Mathematica packages MasterPVA and MasterPVAmulti used to compute \(\lambda \) -brackets in Poisson vertex algebras, which play an important role in the theory of infinite-dimensional Hamiltonian systems. As an application, we give an introduction to the Mathematica package WAlg aimed to compute the \(\lambda \) -brackets among the generators of classical affine \({\mathcal {W}}\) -algebras. The use of these packages is shown by providing some explicit examples. PubDate: 2017-12-09 DOI: 10.1007/s40574-017-0146-9