Monatshefte für Mathematik最新文献

In this paper, we mainly study a new weakly dissipative quasilinear shallow-water waves equation, which can be formally derived from a model with the effect of underlying shear flow from the incompressible rotational two-dimensional shallow water in the moderately nonlinear regime by Wang, Kang and Liu (Appl Math Lett 124:107607, 2022). Considering the dissipative effect, the local well-posedness of the solution to this equation is first obtained by using Kato’s semigroup theory. We then establish the precise blow-up criterion by using the transport equation theory and Moser-type estimates. Moreover, some sufficient conditions which guarantee the occurrence of wave-breaking of solutions are studied according to the different real-valued intervals in which the dispersive parameter (theta ) being located. It is noteworthy that we need to overcome the difficulty induced by complicated nonlocal nonlinear structure and different dispersive parameter ranges to get corresponding convolution estimates.

In our former paper we introduced the concept of localization of ideals in the Fourier algebra of a locally compact Abelian group. It turns out that localizability of a closed ideal in the Fourier algebra is equivalent to the synthesizability of the annihilator of that closed ideal which corresponds to this ideal in the measure algebra. This equivalence provides an effective tool to prove synthesizability of varieties on locally compact Abelian groups. In this paper we utilize this tool to show that when investigating synthesizability of a variety, roughly speaking compact elements of the group can be neglected. Our main result is that spectral synthesis holds on a locally compact Abelian group G if and only if it holds on G/B, where B is the closed subgroup of all compact elements. In particular, spectral synthesis holds on compact Abelian groups. Also we obtain a simple proof for the characterization theorem of spectral synthesis on discrete Abelian groups.

We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg L-functions attached to two cuspidal automorphic representations.

In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get new moment sequences. A class of new sequences is corresponding to a unique symmetric polynomial; if this polynomial is positive, then the new sequence becomes again a moment sequence. We will see for instance that a new sequence generated from minors of a Hankel matrix of a Stieltjes moment sequence is also a Stieltjes moment sequence.

Abstract

In this study, a spectrum (Lambda ) for the integral Sierpinski measures (mu _{M, D}) with the digit set ( D= left{ begin{pmatrix} 0 0 end{pmatrix}, begin{pmatrix} 1 0 end{pmatrix}, begin{pmatrix} 0 1 end{pmatrix}right} ) is derived for a (2 times 2) diagonal matrix M with entries as (3ell _1) and (3ell _4) and for off-diagonal matrix M with both the off-diagonal entries as (3ell ) where, (ell ,ell _1,ell _4 in {mathbb {Z}}{setminus }{{0}}) . Additionally, the spectrum of (mu _{M, D}) for a given M and a generalized digit set D is also examined. The spectrum of self-affine measures (mu _{M, D}) on spatial Sierpinski gasket is obtained when M is diagonal matrix with entries (ell _i in 2{mathbb {Z}}setminus {{0}}) , sign of (ell _i) ’s are same and (D={0, e_1, e_2, e_3}) , where (e_i's ) are the standard basis in ({mathbb {R}}^3) . Further, the spectrum of (mu _{M, D}) for some off-diagonal (3times 3) matrices is also found.

Let H be a complex infinite dimensional Hilbert space, B(H) be the algebra of all bounded linear operators acting on H, and (overline{HC(H)}) ((overline{SC(H)})) be the norm closure of the class of all hypercyclic operators (supercyclic operators) in B(H). An operator (Tin B(H)) is said to be with hypercyclicity (supercyclicity) if T is in (overline{HC(H)}) ((overline{SC(H)})). Using a new spectrum defined from “consistent in invertibility”, this paper gives necessary and sufficient conditions that T is with a-Browder’s theorem or with a-Weyl’s theorem. Further, this paper gives a necessary and sufficient condition that T is a-isoloid, with a-Weyl’s theorem and with hypercyclicity (supercyclicity) concurrently. Also, the relations between that T is with hypercyclicity (supercyclicity) and that T is both with a-Weyl’s theorem and a-isoloid are discussed by means of the new spectrum.

A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity.

Let G denote a compact monothetic group, and let (rho (x) = alpha _k x^k + ldots + alpha _1 x + alpha _0), where (alpha _0, ldots , alpha _k) are elements of G one of which is a generator of G. Let ((p_n)_{nge 1}) denote the sequence of rational prime numbers. Suppose (f in L^{p}(G)) for (p> 1). It is known that if

then the limit (lim _{nrightarrow infty } A_Nf(x)) exists for almost all x with respect Haar measure. We show that if G is connected then the limit is (int _{G} f dlambda ). In the case where G is the a-adic integers, which is a totally disconnected group, the limit is described in terms of Fourier multipliers which are generalizations of Gauss sums.