共查询到20条相似文献,搜索用时 31 毫秒
1.
Let N1 denote the class of generalized Nevanlinna functions with one negative square and let N1, 0 be the subclass of functions Q(z)∈N1 with the additional properties limy→∞ Q(iy)/y=0 and lim supy→∞ y |Im Q(iy)|<∞. These classes form an analytic framework for studying (generalized) rank one perturbations A(τ)=A+τ[·, ω] ω in a Pontryagin space setting. Many functions appearing in quantum mechanical models of point interactions either belong to the subclass N1, 0 or can be associated with the corresponding generalized Friedrichs extension. In this paper a spectral theoretical analysis of the perturbations A(τ) and the associated Friedrichs extension is carried out. Many results, such as the explicit characterizations for the critical eigenvalues of the perturbations A(τ), are based on a recent factorization result for generalized Nevanlinna functions. 相似文献
2.
Let F be a field with ∣F∣ > 2 and Tn(F) be the set of all n × n upper triangular matrices, where n ? 2. Let k ? 2 be a given integer. A k-tuple of matrices A1, …, Ak ∈ Tn(F) is called rank reverse permutable if rank(A1 A2 ? Ak) = rank(Ak Ak−1 ? A1). We characterize the linear maps on Tn(F) that strongly preserve the set of rank reverse permutable matrix k-tuples. 相似文献
3.
Erhard Aichinger 《Journal of Pure and Applied Algebra》2006,205(1):74-93
Let V be a finite expanded group, e.g., a ring or a group. We investigate the near-ring 〈C0(V);+,°〉 of zero-preserving congruence-preserving functions on V. We obtain some information on the structure of 〈C0(V);+,°〉 from the lattice of ideals of V: for example, the number of maximal ideals of 〈C0(V);+,°〉 is completely determined by the isomorphism class of the ideal lattice of V. 相似文献
4.
Hwajong Yoo 《Israel Journal of Mathematics》2016,214(1):359-377
Let CN be the cuspidal subgroup of the Jacobian J0(N) for a square-free integer N > 6. For any Eisenstein maximal ideal m of the Hecke ring of level N, we show that CN[m] ≠ 0. To prove this, we calculate the index of an Eisenstein ideal I contained in m by computing the order of the cuspidal divisor annihilated by I. 相似文献
5.
LetR be a ring. For the setF of all nonzero ideals ofR, we introduce an equivalence relation inF as follows: For idealsI andJ, I~J if and only ifV R (I)=V R(J), whereV R() is the centralizer inR. LetI R=F/~. Then we can see thatn(I R), the cardinality ofI R, is 1 if and only ifR is either a prime ring or a commutative ring (Theorem 1.1). An idealI ofR is said to be a commutator ideal ifI is generated by{st?ts; s∈S, t∈T} for subsetS andT ofR, andR is said to be a ring with (N) if any commutator ideal contains no nonzero nilpotent ideals. Then we have the following main theorem: LetR be a ring with (N). Thenn(I R) is finite if and only ifR is isomorphic to an irredundant subdirect sum ofS⊕Z whereS is a finite direct sum of non commutative prime rings andZ is a commutative ring (Theorem 2.1). Finally, we show that the existence of a ringR such thatn(I R)=m for any given natural numberm. 相似文献
6.
Kazushi Yoshitomi 《Indagationes Mathematicae》2005,16(2):289-299
Let q ∈ {2, 3} and let 0 = s0 < s1 < … < sq = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set lj = sj − sj−1 for j ∈ 1, q. Given (p1,, pq) ∈ Rq, let b: Z → R be a periodic function of period T such that b(·) = pj on sj−1 + 1, sj for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that pm ≠ pn for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1. 相似文献
7.
Let K be the composite field of an imaginary quadratic field Q(ω) of conductor d and a real abelian field L of conductor f distinct from the rationals Q, where (d,f)=1. Let ZK be the ring of integers in K. Then concerning to Hasse's problem we construct new families of infinitely many fields K with the non-monogenic phenomena (1), (2) which supplement (J. Number Theory23 (1986), 347-353; Publ. Math. Fac. Sci Besançon, Theor. Nombres (1984) 25pp) and with monogenic (3). 相似文献
8.
Holly J. Rosson 《Journal of Number Theory》2002,94(1):49-79
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Λ is an order of level M in H, we define theta series for each ideal I of Λ using the reduced norm on H. Using harmonic analysis on the completed algebra H∞ and the arithmetic of quaternion algebras, we establish a transformation law for these theta series. We also define analogs of the classical Hecke operators and show that in general, the Hecke operators map the theta series to a linear combination of theta series attached to different ideals, a generalization of the classical Eichler Commutation Relation. 相似文献
9.
Shih Ping Tung 《Journal of Number Theory》2010,130(4):912-929
In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z. 相似文献
10.
Horst Herrlich 《Topology and its Applications》2011,158(17):2279-2286
Within the framework of Zermelo-Fraenkel set theory ZF, we investigate the set-theoretical strength of the following statements:
- (1)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compactT2space.
- (2)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compact, scattered, T2space.
- (3)
- For every set X, every compactR1topology (itsT0-reflection isT2) on X can be enlarged to a compactT2topology.
- (a)
- (1) implies every infinite set can be split into two infinite sets.
- (b)
- (2) iff AC.
- (c)
- (3) and “there exists a free ultrafilter” iff AC.
11.
Paul Feit 《Israel Journal of Mathematics》1990,69(3):289-320
Letf(X; T 1, ...,T n) be an irreducible polynomial overQ. LetB be the set ofb teZ n such thatf(X;b) is of lesser degree or reducible overQ. Let ?={F j}{F j } j?1 ∞ be a Følner sequence inZ n — that is, a sequence of finite nonempty subsetsF j ?Z n such that for eachvteZ n , $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap (F_j + \upsilon )} \right|}}{{\left| {F_j } \right|}} = 1$ Suppose ? satisfies the extra condition that forW a properQ-subvariety ofP n ?A n and ?>0, there is a neighborhoodU ofW(R) in the real topology such that $\mathop {lim sup}\limits_{j \to \infty } \frac{{\left| {F_j \cap U} \right|}}{{\left| {F_j } \right|}}< \varepsilon $ whereZ n is identified withA n (Z). We prove $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap B} \right|}}{{\left| {F_j } \right|}} = 0$ . 相似文献
12.
Vladimir Piterbarg Goran Popivoda Siniša Stamatović 《Lithuanian Mathematical Journal》2017,57(1):128-141
Let ξ(t), t ∈ [0, T],T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η(t) and μ(t) be other sufficiently smooth random processes independent of ξ(t). In this paper, we obtain an asymptotic exact result for P(sup t∈[0,T](η(t)ξ(t) + μ(t)) > u) as u→∞. 相似文献
13.
Yuk-Kam Lau 《Journal of Number Theory》2002,96(2):400-416
Given the orthonormal basis of Hecke eigenforms in S2k(Γ(1)), Luo established an associated probability measure dμk on the modular surface Γ(1)\H that tends weakly to the invariant measure on Γ(1)\H. We generalize his result to the arithmetic surface Γ0(N)\H where N?1 is square-free 相似文献
14.
Let A be a d × d expansive matrix with ∣detA∣ = 2. This paper addresses Parseval frame wavelets (PFWs) in the setting of reducing subspaces of L2(Rd). We prove that all semi-orthogonal PFWs (semi-orthogonal MRA PFWs) are precisely the ones with their dimension functions being non-negative integer-valued (0 or 1). We also characterize all MRA PFWs. Some examples are provided. 相似文献
15.
Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) x) is considered, as x →∞. 相似文献
16.
Fractal functions and interpolation 总被引:1,自引:0,他引:1
Michael F. Barnsley 《Constructive Approximation》1986,2(1):303-329
Let a data set {(x i,y i) ∈I×R;i=0,1,?,N} be given, whereI=[x 0,x N]?R. We introduce iterated function systems whose attractorsG are graphs of continuous functionsf∶I→R, which interpolate the data according tof(x i)=y i fori ε {0,1,?,N}. Results are presented on the existence, coding theory, functional equations and moment theory for such fractal interpolation functions. Applications to the approximation of naturally wiggly functions, which may show some kind of geometrical self-similarity under magnification, such as profiles of cloud tops and mountain ranges, are envisaged. 相似文献
17.
Michel Weber 《Indagationes Mathematicae》2007,18(2):281-293
Let ?= {?i,i ≥1} be a sequence of independent Bernoulli random variables (P{?i = 0} = P{?i = 1 } = 1/2) with basic probability space (Ω, A, P). Consider the sequence of partial sums Bn=?1+...+?n, n=1,2..... We obtain an asymptotic estimate for the probability P{P-(Bn) > >} for >≤ne/log log n, c a positive constant. 相似文献
18.
Keaitsuda Maneeruk 《Journal of Mathematical Analysis and Applications》2005,306(1):218-226
Let M denote the class of functions f meromorphic outside some compact totally disconnected set E=E(f) and the cluster set of f at any a∈E with respect to is equal to . It is known that class M is closed under composition. Let f and g be two functions in class M, we study relationship between dynamics of f○g and g○f. Denote by F(f) and J(f) the Fatou and Julia sets of f. Let U be a component of F(f○g) and V be a component of F(g○f) which contains g(U). We show that under certain conditions U is a wandering domain if and only if V is a wandering domain; if U is periodic, then so is V and moreover, V is of the same type according to the classification of periodic components as U unless U is a Siegel disk or Herman ring. 相似文献
19.
20.
S. A. Gritsenko 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):65-87
Let N 0(T) be the number of zeros of the Davenport–Heilbronn function in the interval [1/2, 1/2+ i T]. It is proved that N 0(T) ? T (ln T)1/2+1/16?ε, where ε is an arbitrarily small positive number. 相似文献