共查询到20条相似文献,搜索用时 433 毫秒
1.
D. A. Tuganbaev 《Journal of Mathematical Sciences》2008,149(3):1286-1337
This is a study of ring-theoretic properties of a Laurent ring over a ring A, which is defined to be any ring formed from the additive group of Laurent series in a variable x over A, such that left multiplication by elements of A and right multiplication by powers of x obey the usual rules, and such that the lowest degree of the product of two nonzero series is not less than the sum of the
lowest degrees of the factors. The main examples are skew-Laurent series rings A((x; ϕ)) and formal pseudo-differential operator rings A((t
−1; δ)), with multiplication twisted by either an automorphism ϕ or a derivation δ of the coefficient ring A (in the latter case, take x = t
−1). Generalized Laurent rings are also studied. The ring of fractional n-adic numbers (the localization of the ring of n-adic integers with respect to the multiplicative set generated by n) is an example of a generalized Laurent ring. Necessary and/or sufficient conditions are derived for Laurent rings to be
rings of various standard types. The paper also includes some results on Laurent series rings in several variables.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 3, pp. 151–224, 2006. 相似文献
2.
Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients
off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated. 相似文献
3.
D. Yu. Pochekutov 《Siberian Mathematical Journal》2009,50(6):1081-1091
We consider the problem of the algebraicity of diagonal series for the Laurent expansions of rational functions, geometrically
identifiable using the amoeba of the denominator or an integer point in its Newton polyhedron. We give sufficient conditions
for the algebraicity of diagonals basing on the theory of multidimensional residues and topological properties of the complements
to collections of complex hypersurfaces in complex analytic varieties. 相似文献
4.
Dirk Segers 《Mathematische Zeitschrift》2006,252(2):429-455
Let K be a p-adic field. We explore Igusa's p-adic zeta function, which is associated to a K-analytic function on an open and compact subset of Kn. First we deduce a formula for an important coefficient in the Laurent series of this meromorphic function at a candidate
pole. Afterwards we use this formula to determine all values less than −1/2 for n=2 and less than −1 for n=3 which occur as the real part of a pole. 相似文献
5.
Jan Uliczka 《manuscripta mathematica》2010,132(1-2):159-168
In this article we discuss a result on formal Laurent series and some of its implications for Hilbert series of finitely generated graded modules over standard-graded polynomial rings: For any integer Laurent function of polynomial type with non-negative values the associated formal Laurent series can be written as a sum of rational functions of the form ${\frac{Q_j(t)}{(1-t)^j}}$ , where the numerators are Laurent polynomials with non–negative integer coefficients. Hence any such series is the Hilbert series of some finitely generated graded module over a suitable polynomial ring ${\mathbb{F}[X_1 , \ldots , X_n]}$ . We give two further applications, namely an investigation of the maximal depth of a module with a given Hilbert series and a characterization of Laurent polynomials which may occur as numerator in the presentation of a Hilbert series as a rational function with a power of (1 ? t) as denominator. 相似文献
6.
Yu. N. Frolov 《Mathematical Notes》1971,9(5):301-307
A system of functions, biorthogonal to the D-basis introduced by M. K. Fage for a linear differential operator D with analytic coefficients, is constructed. Series in the combination of the D-basis with this system generalize Laurent series in the same way as series in the D-basis generalize Taylor series.Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 521–531, May, 1971. 相似文献
7.
Fuensanta Aroca 《Proceedings of the American Mathematical Society》2004,132(10):3035-3045
We prove the existence of local Puiseux-type parameterizations of complex analytic sets via Laurent series convergent on wedges. We describe the wedges in terms of the Newton polyhedron of a function vanishing on the discriminant locus of a projection. The existence of a local parameterization of quasi-ordinary singularities of complex analytic sets of any codimension will come as a consequence of our main result.
8.
K. A. Grasse 《Journal of Optimization Theory and Applications》1983,40(2):221-235
In this paper, we consider extremal solutions of multivalued differential equations, i.e., solutions that steer to the boundary of the attainable set. Multivalued differential equations arise in a natural way from control systems governed by ordinary differential equations that have a variable control-constraint set. Extremal solutions of multi-valued differential equations are important in the study of the optimal control of such systems. We give conditions under which extremality of a solution at a certain time implies extremality of the solution at all previous times where it is defined. Necessary conditions for extremality are also obtained. We treat both the time-dependent case and the time-independent case. 相似文献
9.
We consider random analytic functions defined on the unit disk of the complex plane f(z) = ?n=0¥ an Xn znf(z) = \sum_{n=0}^{\infty} a_{n} X_{n} z^{n}, where the X
n
’s are i.i.d., complex-valued random variables with mean zero and unit variance. The coefficients a
n
are chosen so that f(z) is defined on a domain of ℂ carrying a planar or hyperbolic geometry, and Ef(z)[`(f(w))]\mathbf{E}f(z)\overline{f(w)} is covariant with respect to the isometry group. The corresponding Gaussian analytic functions have been much studied, and
their zero sets have been considered in detail in a monograph by Hough, Krishnapur, Peres, and Virág. We show that for non-Gaussian
coefficients, the zero set converges in distribution to that of the Gaussian analytic functions as one transports isometrically
to the boundary of the domain. The proof is elementary and general. 相似文献
10.
Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated. 相似文献
11.
We study the skew inverse Laurent-serieswise Armendariz (or simply, SIL-Armendariz) condition on R, a generalization of the standard Armendariz condition from polynomials to skew inverse Laurent series. We study relations between the set of annihilators in R and the set of annihilators in R((x ?1; α)). Among applications, we show that a number of interesting properties of a SIL-Armendariz ring R such as the Baer and the α-quasi Baer property transfer to its skew inverse Laurent series extensions R((x ?1; α)) and vice versa. For an α-weakly rigid ring R, R((x ?1; α)) is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S ?(R) has a generalized countable join in R. Various types of examples of SIL-Armendariz rings is provided. 相似文献
12.
We consider the infinite series in Wick powers of a generalized free field that are convergent under smoothing with analytic test functions and realize a nonlocal extension of the Borchers equivalence classes. The nonlocal fields to which the Wick power series converge are proved to be asymptotically commuting. This property serves as a natural generalization of the relative locality of the Wick polynomials. The proposed proof is based on exploiting the analytic properties of the vacuum expectation values in the x space and applying the Cauchy–Poincaré theorem. 相似文献
13.
D. S. Lubinsky 《Constructive Approximation》2002,18(2):285-308
Let a≥ 0 , ɛ >0 . We use potential theory to obtain a sharp lower bound for the linear Lebesgue measure of the set Here P is an arbitrary polynomial of degree ≤ n . We then apply this to diagonal and ray Padé sequences for functions analytic (or meromorphic) in the unit ball. For example,
we show that the diagonal \left{ [n/n]\right}
n=1
∞
sequence provides good approximation on almost one-eighth of the circles centre 0 , and the \left{ [2n/n]\right}
n=1
∞
sequence on almost one-quarter of such circles.
July 18, 2000. Date revised: . Date accepted: April 19, 2001. 相似文献
14.
Laurent-Padé (Chebyshev) rational approximantsP
m
(w, w
−1)/Q
n
(w, w
−1) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP
m
/Q
n
matches that of a given functionf(w, w
−1) up to terms of orderw
±(m+n)
, based only on knowledge of the Laurent series coefficients off up to terms inw
±(m+n)
. This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent
series ofP
m
matches that ofQ
n
f up to terms of orderw
±(m+n
), but based on knowledge of the series coefficients off up to terms inw
±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and
corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of
the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations
are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably
similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the
use of either. 相似文献
15.
Xiao-Xiong Gan Dariusz Bugajewski 《Bulletin of the Brazilian Mathematical Society》2011,42(3):415-437
Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets
up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication
between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent
series, denoted by
\mathbbL\mathbb{L}. By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series
with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus
about formal Laurent series is also introduced. 相似文献
16.
We give an explicit analytic expression for the S-matrix in the case of an arbitrary central interaction inside a sphere of finite radius with a Yukawa-potential tail at large
distances. The method uses the completeness of the wave functions outside the finite sphere and also the unitarity and the
symmetry conditions for the S-matrix.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 113–128, April, 2006. 相似文献
17.
Siberian Mathematical Journal - We obtain some new estimates that show the extremality of the Rademacher system in the set of sequences of independent functions considered in rearrangement... 相似文献
18.
Senior Researcher Sorin Radnef 《PAMM》2006,6(1):651-652
This paper state an analytic solution for non-autonomous linear ODE of order n, expressed as a power series with analytic coefficients, determined by recurrence formulae. The result is compared with that for n = 1 and is applied for a particular ODE, of order n = 2, which has an explicit solution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
20.
We prove that almost all (with respect to Haar measure) formal Laurent series are approximated with the linear order −(degβ)n by their β-expansions convergents. Hausdorff dimensions of sets of Laurent series which are approximated by all other orders, are determined. In contrast, the corresponding theory of real case has not been established. 相似文献