共查询到20条相似文献,搜索用时 31 毫秒
1.
On Schwarzian Triangle Functions,Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations
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Li Chien Shen 《数学学报(英文版)》2018,34(11):1648-1662
Let G be the group of the fractional linear transformations generated by where m, n is a pair of integers with either n ≥ 2,m ≥ 3 or n ≥ 3,m ≥ 2; τ lies in the upper half plane H.
A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan’s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions. 相似文献
$$T(\tau ) = \tau + \lambda ,S(\tau ) = \frac{{\tau \cos \frac{\pi }{n} + \sin \frac{\pi }{n}}}{{ - \tau \sin \frac{\pi }{n} + \cos \frac{\pi }{n}}};$$
$$\lambda = 2\frac{{\cos \frac{\pi }{m} + \cos \frac{\pi }{n}}}{{\sin \frac{\pi }{n}}};$$
2.
Rafael de la Llave 《Regular and Chaotic Dynamics》2017,22(6):650-676
We present simple proofs of a result of L.D. Pustylnikov extending to nonautonomous dynamics the Siegel theorem of linearization of analytic mappings. We show that if a sequence f n of analytic mappings of C d has a common fixed point f n (0) = 0, and the maps f n converge to a linear mapping A∞ so fast that then f n is nonautonomously conjugate to the linearization. That is, there exists a sequence h n of analytic mappings fixing the origin satisfying The key point of the result is that the functions hn are defined in a large domain and they are bounded. We show that We also provide results when f n converges to a nonlinearizable mapping f∞ or to a nonelliptic linear mapping. In the case that the mappings f n preserve a geometric structure (e. g., symplectic, volume, contact, Poisson, etc.), we show that the hn can be chosen so that they preserve the same geometric structure as the f n . We present five elementary proofs based on different methods and compare them. Notably, we consider the results in the light of scattering theory. We hope that including different methods can serve as an introduction to methods to study conjugacy equations.
相似文献
$$\sum\limits_n {{{\left\| {{f_m} - {A_\infty }} \right\|}_{L\infty \left( B \right)}} < \infty } $$
$${A_\infty } = diag\left( {{e^{2\pi i{\omega _1}}},...,{e^{2\pi i{\omega _d}}}} \right)\omega = \left( {{\omega _1},...,{\omega _q}} \right) \in {\mathbb{R}^d},$$
$${h_{n + 1}} \circ {f_n} = {A_\infty }{h_n}.$$
$${\sum\nolimits_n {\left\| {{h_n} - Id} \right\|} _{L\infty (B)}} < \infty .$$
3.
Let X be a real normed space and let f: ? → X be a continuous mapping. Let T f (t 0) be the contingent of the graph G(f) at a point (t 0, f(t 0)) and let S + ? (0,∞) × X be the “right” unit hemisphere centered at (0, 0 X ). We show that
相似文献
- 1.If dimX < ∞ and the dilation D(f, t 0) of f at t 0 is finite then T f (t 0) ∩ S + is compact and connected. The result holds for \(T_f (t_0 ) \cap \overline {S^ + } \) even with infinite dilation in the case f: [0,∞) → X.
- 2.If dimX = ∞, then, given any compact set F ? S +, there exists a Lipschitz mapping f: ? → X such that T f (t 0) ∩ S + = F.
- 3.But if a closed set F ? S + has cardinality greater than that of the continuum then the relation T f (t 0) ∩ S + = F does not hold for any Lipschitz f: ? → X.
4.
For a countable, weakly minimal theory T, we show that the Schröder-Bernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following:
We conclude that for countable, weakly minimal theories, the Schröder-Bernstein property is absolute between transitve models of ZFC. 相似文献
- 1.For any U-rank-1 type q ∈ S(acl eq (?)) and any automorphism f of the monster model C, there is some n < ω such that f n (q) is not almost orthogonal to q ? f(q) ? … ? f n?1(q)
- 2.T has no infinite collection of models which are pairwise elementarily bi-embeddable but pairwise nonisomorphic.
5.
Let A denote the class of functions f(z) with
f(0)=f′(0)−1=0, 相似文献
6.
On solutions of a common generalization of the Go?a?b-Schinzel equation and of the addition formulae
Anna Mureńko 《Journal of Mathematical Analysis and Applications》2008,341(2):1236-1240
Under some additional assumptions we determine solutions of the equation
f(x+M(f(x))y)=f(x)○f(y), 相似文献
7.
Lothar Berg 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3305-3310
The paper deals with the functional equation
f(x)=F(f(u(x)),f(v(x))) 相似文献
8.
Justyna Sikorska 《Journal of Mathematical Analysis and Applications》2005,311(1):209-217
We study the stability problem for mappings satisfying the equation
‖f(x−y)‖=‖f(x)−f(y)‖. 相似文献
9.
Let X and Y be two Banach spaces, and f: X → Y be a standard ε-isometry for some ε ≥ 0. In this paper, by using a recent theorem established by Cheng et al. (2013–2015), we show a sufficient condition guaranteeing the following sharp stability inequality of f: There is a surjective linear operator T: Y → X of norm one so that
$$\left\| {Tf(x) - x} \right\| \leqslant 2\varepsilon , for all x \in X.$$
As its application, we prove the following statements are equivalent for a standard ε-isometry f: X → Y:
This gives an affirmative answer to a question proposed by Vestfrid (2004, 2015). 相似文献
- (i)lim inf t→∞ dist(ty, f(X))/|t| < 1/2, for all y ∈ S Y ;
- (ii)\(\tau(f)\equiv sup_{y\epsilon S_{Y}}\) lim inf t→∞dist(ty, f(X))/|t| = 0;
- (iii)there is a surjective linear isometry U: X → Y so that$$\left\| {f(x) - Ux} \right\| \leqslant 2\varepsilon , for all x \in X.$$
10.
Let q be a prime power. For a divisor n of q ? 1 we prove an asymptotic formula for the number of polynomials of the formsuch that the five (not necessarily different) polynomials f(X), f(X)±X and f(f(X))±X are all permutation polynomials over \({\mathbb{F}_q}\) . Such polynomials can be used to define check digit systems that detect the most frequent errors: single errors, adjacent transpositions, jump transpositions, twin errors and jump twin errors.
相似文献
$f(X)=\frac{a-b}{n}\left(\sum_{j=1}^{n-1}X^{j(q-1)/n}\right)X+\frac{a+b(n-1)}{n}X\in\mathbb{F}_q[X]$
11.
In the space L 2 of real-valued measurable 2π-periodic functions that are square summable on the period [0, 2π], the Jackson-Stechkin inequality , is considered, where E n (f) is the value of the best approximation of the function f by trigonometric polynomials of order at most n and ω(δ, f) is the modulus of continuity of the function f in L 2 of order 1 or 2. The value is found at the points δ = 2π/m (where m ∈ ?) for m ≥ 3n 2 + 2 and ω = ω 1 as well as for m ≥ 11n 4/3 ? 1 and ω = ω 2.
相似文献
$$E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2 $$
$$\mathcal{K}_n (\delta ,\omega ) = \sup \left\{ {\frac{{E_n (f)}}{{\omega (\delta ,f)}}:f \in L^2 } \right\}$$
12.
This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation where \(c\ge 0\) is a constant and the functions a and f are continuous and not necessarily periodic in t. Under other suitable assumptions on a and f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.
相似文献
$$\begin{aligned} u^{\prime \prime }+cu^{\prime }-a(t)u+f(t,u)=0, \end{aligned}$$
13.
Eliza Jab?ońska 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2465-572
Let X be a separable F-space over the field K of reals or complex numbers. We characterize solutions of the equation
f(x+M(f(x))y)=f(x)f(y) 相似文献
14.
Young Whan Lee Byung Mun Choi 《Journal of Mathematical Analysis and Applications》2004,299(2):305-313
We obtain the super stability of Cauchy's gamma-beta functional equation
B(x,y)f(x+y)=f(x)f(y), 相似文献
15.
Justyna Sikorska 《Journal of Mathematical Analysis and Applications》2010,372(1):99-109
We study the stability of an equation in a single variable of the form
f(x)=af(h(x))+bf(−h(x)) 相似文献
16.
A. I. Noarov 《Differential Equations》2009,45(2):197-208
We study the stationary Focker-Planck equation Δu ? div(u f) = 0 with a given vector field f of the class C 0 ∞ (R n ) on the basis of a fixed point principle that generalizes the contraction mapping method. Next, we introduce a parameter in the equation and prove the unique solvability of the equation Δu ? div(uγ f) = 0 with the parameter in the class of positive slowly increasing functions. We reveal the analytic dependence of the positive solution u on the parameter γ. Pointwise estimates for positive solutions are proved. 相似文献
17.
Poo-Sung Park 《Aequationes Mathematicae》2018,92(3):487-495
P. V. Chung showed that there are many multiplicative functions f which satisfy \(f(m^2+n^2) = f(m^2)+f(n^2)\) for all positive integers m and n. In this article, we show that if more than 2 squares in the additive condition are involved, then such f is uniquely determined. That is, if a multiplicative function f satisfies for arbitrary positive integers \(a_i\), then f is the identity function. In this sense, we call the set of all positive squares a k-additive uniqueness set for multiplicative functions.
相似文献
$$\begin{aligned} f(a_1^2 + a_2^2 + \cdots + a_k^2) = f(a_1^2) + f(a_2^2) + \cdots + f(a_k^2) \end{aligned}$$
18.
Consider the second order discrete Hamiltonian systems Δ2u(n-1)-L(n)u(n) + ▽W (n, u(n)) = f(n),where n ∈ Z, u ∈ RN and W : Z × RN → R and f : Z → RN are not necessarily periodic in n. Under some comparatively general assumptions on L, W and f , we establish results on the existence of homoclinic orbits. The obtained results successfully generalize those for the scalar case. 相似文献
19.
Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2011,373(1):227-234
For a function f defined in an interval I, satisfying the conditions ensuring the existence and uniqueness of the Lagrange mean L[f], we prove that there exists a unique two variable mean M[f] such that
20.
In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equations
f(k)+Ak−1f(k−1)+?+A0f=0 相似文献