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1.
Let f be a cusp form of the Hecke space
and let L
f
be the normalized L-function associated to f. Recently it has been proved that L
f
belongs to an axiomatically defined class of functions
. We prove that when λ ≤ 2, L
f
is always almost primitive, i.e., that if L
f
is written as product of functions in
, then one factor, at least, has degree zeros and hence is a Dirichlet polynomial. Moreover, we prove that if
then L
f
is also primitive, i.e., that if L
f
= F
1
F
2 then F
1 (or F
2) is constant; for
the factorization of non-primitive functions is studied and examples of non-primitive functions are given. At last, the subset
of functions f for which L
f
belongs to the more familiar extended Selberg class
is characterized and for these functions we obtain analogous conclusions about their (almost) primitivity in
. 相似文献
2.
Let H be an atomic monoid. For let denote the set of all with the following property: There exist atoms (irreducible elements) u
1, …, u
k
, v
1, …, v
m
∈ H with u
1· … · u
k
= v
1 · … · v
m
. We show that for a large class of noetherian domains satisfying some natural finiteness conditions, the sets are almost arithmetical progressions. Suppose that H is a Krull monoid with finite cyclic class group G such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number
fields). We show that, for every , max which settles Problem 38 in [4].
Authors’ addresses: W. Gao, Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China; A. Geroldinger, Institut
für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit?t Graz, Heinrichstra?e 36, 8010 Graz, Austria 相似文献
3.
L. Olsen 《Monatshefte für Mathematik》2008,155(2):191-203
In this paper we consider the relationship between the topological dimension
and the lower and upper q-Rényi dimensions
and
of a Polish space X for q ∈ [1, ∞]. Let
and
denote the Hausdorff dimension and the packing dimension, respectively. We prove that
for all analytic metric spaces X (whose upper box dimension is finite) and all q ∈ (1, ∞); of course, trivially,
for all q ∈ [1, ∞]. As a corollary to this we obtain the following result relating the topological dimension and the lower and upper
q-Rényi dimensions:
for all Polish spaces X and all q ∈ [1, ∞]; in (1) and (2) we have used the following notation, namely, for two metric spaces X and Y, we write X ∼ Y if and only if X is homeomorphic to Y. Equality (1) has recently been proved for q = ∞ by Myjak et al.
Author’s address: Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland 相似文献
4.
Given an almost complex structure J in a cylinder of
(p > 1) together with a compatible symplectic form
and given an arbitrary J-holomorphic curve
without boundary in that cylinder, we construct an holomorphic perturbation of
, for the canonical complex structure J
0 of
, such that the distance between these two curves in W
1,2 and
norms, in a sub-cylinder, are controled by quantities depending on J,
and by the area of
only. These estimates depend neither on the topology nor on the conformal class of
. They are key tools in the recent proof of the regularity of 1-1 integral currents in [RT].Received: 2 October 2003, Accepted: 18 November 2003, Published online: 25 February 2004 相似文献
5.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
6.
7.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
8.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
9.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
10.
11.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
12.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
, where
is a continuous function with
,
runs over
, the set of Farey fractions of order Q in the unit interval [0,1] and
are consecutive elements of
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
13.
Let p be a prime number.
Let G be a finite
p-group and
. Denote by
the complex conjugate of
. Assume that
. We show that the number of
distinct irreducible constituents of the product
is at least
.
Received: 17 March 2003 相似文献
14.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
15.
Let
be a simply connected domain in
, such that
is connected. If g is holomorphic in Ω and every derivative of g extends continuously on
, then we write g ∈ A∞ (Ω). For g ∈ A∞ (Ω) and
we denote
. We prove the existence of a function f ∈ A∞(Ω), such that the following hold:
相似文献
i) | There exists a strictly increasing sequence μn ∈ {0, 1, 2, …}, n = 1, 2, …, such that, for every pair of compact sets Γ, Δ ⊂ and every l ∈ {0, 1, 2, …} we have |
ii) | For every compact set with and Kc connected and every function continuous on K and holomorphic in K0, there exists a subsequence of , such that, for every compact set we have |
16.
Given any R-semimodule M equipped with a semitopology
we construct an N-protosummation
for M. If
satisfies certain properties, then a similar construction leads to an unconditional N-summation
for M, that is an N-summation for M equipped with the trivial prenorm MD over the N-summation (DN,D) for D. Conversely any N-protosummation
on M gives rise to a topology
. If both
and
satisfy a certain separation property, then
and
form a Galois connection.
Dedicated to my friend and collegue Nico Pumplün on the occasion of his 70th birthdayMathematics Subject Classifications (2000) 16Y60, 54A05. 相似文献
17.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
18.
19.
YunYanYANG 《数学学报(英文版)》2003,19(1):63-68
In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions. 相似文献
20.
The N-commutator
is conjecturally a well-defined nontrivial operation on
for x =
(x
1, ... ,
x
n
)
if and only if N =
n
2 +
2n - 2. This is
proved for n = 2 and confirmed by
computer experiments for n < 5.
Under 2- and 5-commutators the algebra of divergence-free
vector fields in two dimensions is an sh-Lie (strong homotopic
Lie) algebra in the sense of Stasheff. Similarly,
W(2) is an
sh-Lie algebra with respect to 2- and 6-commutators. 相似文献