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2.
The main result of this paper is that if a sequence of complex numbers (a
n)n≥0 satisfies
and % MathType!MTEF!2!1!+-
for some integerr≥0, thena
n=0 for alln>r. As an application, we deduce a localized form of a theorem of Allan about nilpotent elements in Banach algebras, and this
in turn leads to an invariant-subspace theorem. As a further application, we prove a variant of Carleman's theorem on the
unique determination of probability distributions by their moments. The paper concludes with a quantitative form of the main
result.
Research supported by grants from the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR of Québec,
and the Ministry of Education of Québec (co-opération Québec-France). 相似文献
3.
Erhard Aichinger 《Monatshefte für Mathematik》2004,143(2):89-103
We show that the variety of near-rings and the variety of zero-symmetric near-rings are both generated by their finite members. We show this in a more general context: if a variety
is generated by a class of algebras
, then the variety of
-composition algebras is generated by the class of all full function algebras on direct products of finitely many copies of algebras in
. 相似文献
4.
Bruno Pini 《Annali di Matematica Pura ed Applicata》1959,48(1):305-332
Sunto Si studia il problema della determinazione di una soluzione dell'equazione
ak(x)∂ku/∂xk=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x1, x2, b (a<x1<x2<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione
ak(x)∂ku/∂xk+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x1, x2, b e la cui ∂/∂y assuma assegnati valori per y=0.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
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6.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2002,42(4):425-448
LetA be a positive self-adjoint operator and letB be anm-accretive operator which isA-small with a relative bound less than one. LetH=A+B, thenH is well-defined on dom(H)=dom(A) andm-accretive. IfB is a strictlym-accretive operator obeying
then for the Trotter product formula we prove that
(and similar forH
*) asn, uniformly int0. We also show that: (a) theA-smallness ofB guarantees the condition (1) for (0,1/2), i.e. the estimate (2) holds for (0,1/2); (b) ifB is strictlym-sectorial, then there are sufficient conditions ensuring the relation (1) for =1/2, that implies (2); (c) ifB isA-small,m-sectorial and such that dom(A
1/2) is a subset of the formdomain ofB, then again (2) is valid for =1/2. 相似文献
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((2)) |
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8.
Luis Arenas-Carmona 《Archiv der Mathematik》2008,91(6):486-491
It is known that classes of indefinite quadratic forms in a genus are classified by the Galois group of a spinor class field
[4]. Hsia has proved the existence of a representation field F with the property that a lattice in the genus represents a fixed given lattice if and only if the corresponding element of
the Galois group is trivial on F. Spinor class fields can also be used to classify conjugacy classes of maximal orders in a central simple algebra. In [1]
we left open the issue of whether for every fixed given non-maximal order in a central simple division algebra there exists a representation field L with the property that embeds into a given maximal order if and only if the corresponding element of the Galois group is trivial on L. In this work we give a negative answer to this question for central simple division algebras of dimension ≥ 32. The case of non-division algebras is also treated by replacing the phrase embeds into by is contained in a conjugate of. As a byproduct of the techniques used in this paper we compute the representation field of an Eichler order in a quaternion
algebra.
Received: 8 April 2008 相似文献
9.
A. Dosiev 《Journal of Mathematical Sciences》2004,124(2):4886-4908
Topological algebras of (convergent) power series of elements of a Lie algebra are introduced and the existence of continuous homomorphisms of these algebras into an operator algebra is studied. For the Slodkowski spectra, the spectral mapping theorem
is proved for generators a of a finite-dimensional nilpotent Lie algebra of bounded linear operators under the condition that a family f of elements of a power series algebra is finite-dimensional. Bibliography: 22 titles. 相似文献
10.
K. Farahmand 《Journal of Theoretical Probability》2003,16(2):419-426
There is both mathematical and physical interest in the behaviour of the polynomial of the form
. The coefficients a
j
, j = 0,...,n are assumed to be independent normally distributed random variables with mean zero and variance
2. In this paper by using the motion of exceedence measure for stochastic processes, for n large, we derive an asymptotic estimate for the expected area of the curve representing the above polynomial cut off by the x-axis. We show that our method can be used to obtain results for similar random polynomials. 相似文献
11.
Many-valued quantum algebras 总被引:1,自引:0,他引:1
We deal with algebras of the same signature as MV-algebras which are a common extension of MV-algebras and orthomodular lattices, in the sense
that (i) A bears a natural lattice structure, (ii) the elements a for which is a complement in the lattice form an orthomodular sublattice, and (iii) subalgebras whose elements commute are MV-algebras.
We also discuss the connections with lattice-ordered effect algebras and prove that they form a variety.
Supported by the Research and Development Council of the Czech Government via the project MSM6198959214. 相似文献
12.
We study higher-dimensional analogs of the Dedekind–Carlitz polynomials
, where u and v are indeterminates and a and b are positive integers. Carlitz proved that these polynomials satisfy the reciprocity law
from which one easily deduces many classical reciprocity theorems for the Dedekind sum and its generalizations. We illustrate
that Dedekind–Carlitz polynomials appear naturally in generating functions of rational cones and use this fact to give geometric
proofs of the Carlitz reciprocity law and various extensions of it. Our approach gives rise to new reciprocity theorems and
computational complexity results for Dedekind–Carlitz polynomials, a characterization of Dedekind–Carlitz polynomials in terms
of generating functions of lattice points in triangles, and a multivariate generalization of the Mordell–Pommersheim theorem
on the appearance of Dedekind sums in Ehrhart polynomials of 3-dimensional lattice polytopes.
Research of Haase supported by DFG Emmy Noether fellowship HA 4383/1. We thank Robin Chapman, Eric Mortenson, and an anonymous
referee for helpful comments. 相似文献
13.
Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods 总被引:8,自引:3,他引:5
Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)K×K such that
where T: K×KH is a nonlinear mapping on K×K. 相似文献
14.
Bang-He Li 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(6):959-968
There are lots of results on the solutions of the heat equation
but much less on those of the Hermite heat equation
due to that its coefficients are not constant and even not bounded. In this paper, we find an explicit relation between the
solutions of these two equations, thus all known results on the heat equation can be transferred to results on the Hermite
heat equation, which should be a completely new idea to study the Hermite equation. Some examples are given to show that known
results on the Hermite equation are obtained easily by this method, even improved. There is also a new uniqueness theorem
with a very general condition for the Hermite equation, which answers a question in a paper in Proc. Japan Acad. (2005).
Supported partially by 973 project (2004CB318000) 相似文献
15.
In this paper we consider the weakly coupled elliptic system with critical growth
where a, b, c, d are C
1-functions defined in a bounded regular domain of
N
. Here we construct families of solutions which blow-up and concentrate at some points in as the positive parameter goes to zero.*The authors are supported by M.I.U.R., project Metodi variazionali e topologici nello studio di fenomeni non lineari. 相似文献
16.
D. M. Smirnov 《Algebra and Logic》2004,43(2):128-131
It is proved that for every regular variety V of algebras, an interpretability type [V] in the lattice
is primary w.r.t. intersection, and so has at most one covering. Moreover, the sole covering, if any, for [V] is necessarily infinite. For a locally finite regular variety V, [V] has no covering. Cyclic varieties of algebras turn out to be particularly interesting among the regular. Each of these is a variety of n-groupoids (A; f) defined by an identity
, where is an n-cycle of degree n 2. Interpretability types of the cyclic varieties form, in
, a subsemilattice isomorphic to a semilattice of square-free natural numbers n 2, under taking m n=[m,n] (l.c.m.). 相似文献
17.
A generalized BL - algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities
. It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct
products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute
with all other elements.
Subsequently we construct subdirectly irreducible noncommutative integral GBL-algebras that are not ordinal sums of generalized
MV-algebras. We also give equational bases for the varieties generated by such algebras. The construction provides a new way
of order-embedding the lattice of
-group varieties into the lattice of varieties of integral GBLalgebras.
The results of this paper also apply to pseudo-BL algebras.
This paper is dedicated to Walter Taylor.
Received March 7, 2005; accepted in final form July 25, 2005. 相似文献
18.
We consider semilinear partial differential equations in ℝ
n
of the form
$
\sum\limits_{\frac{{|\alpha |}}
{m} + \frac{{|\beta |}}
{k} \leqslant 1} {c_{\alpha \beta } x^\beta D_x^\alpha u = F(u)} ,
$
\sum\limits_{\frac{{|\alpha |}}
{m} + \frac{{|\beta |}}
{k} \leqslant 1} {c_{\alpha \beta } x^\beta D_x^\alpha u = F(u)} ,
相似文献
19.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
20.
We prove a new approximation theorem, which enables us to show that the relaxed energy
of Sobolev mappings u from higher dimensional balls into S2 is given by
, provided their singular set is of Lebesgue measure zero. Here
is the mass of the minimal integer multiplicity connection associated to the singularity current Su of u. Using this approximation theorem, we prove a partial regularity theorem for minimizers of the relaxed energy functional.Received: 5 May 2004, Accepted: 19 October 2004, Published online: 10 December 2004 相似文献
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