共查询到20条相似文献,搜索用时 46 毫秒
1.
Let A denote the class of functions f(z) with
f(0)=f′(0)−1=0, 相似文献
2.
In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak−1 is the dominant coefficient, then every transcendental solution f(z) of equation
satisfies λ(f) = ∞, where λ(f) denotes the exponent of convergence of zeros of the meromorphic function f(z). 相似文献
f(k)+Ak-1 f(k-1)+?+A0 f=0
3.
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
4.
Xiaoling Wang Chung-Chun Yang 《Journal of Mathematical Analysis and Applications》2006,324(1):373-380
We investigate the factorization of entire solutions of the following algebraic differential equations:
bn(z)finjn(f′)+bn−1(z)fin−1jn−1(f′)+?+b0(z)fi0j0(f′)=b(z), 相似文献
5.
Stevo Stevi? 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2448-2454
Bergman-Privalov class ANα(B) consists of all holomorphic functions on the unit ball B⊂Cn such that
‖f‖ANα:=∫Bln(1+∣f(z)∣)dVα(z)<∞, 相似文献
6.
S. Ponnusamy A. Vasudevarao 《Journal of Mathematical Analysis and Applications》2007,332(2):1323-1334
Let F1 (F2 respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f′(0)−1 satisfying the condition RePf(z)<3/2 (RePf(z)>−1/2 respectively) in |z|<1, where Pf(z)=1+zf″(z)/f′(z). For any fixed z0 in the unit disk and λ∈[0,1), we shall determine the region of variability for logf′(z0) when f ranges over the class and , respectively. 相似文献
7.
For ?1≤B<A≤1, let \(\mathcal {S}^{*}(A,B)\) denote the class of normalized analytic functions \(f(z)= z+{\sum }_{n=2}^{\infty }a_{n} z^{n}\) in |z|<1 which satisfy the subordination relation z f ′(z)/f(z)?(1 + A z)/(1 + B z) and Σ?(A,B) be the corresponding class of meromorphic functions in |z|>1. For \(f\in \mathcal {S}^{*}(A,B)\) and λ>0, we shall estimate the absolute value of the Taylor coefficients a n (?λ,f) of the analytic function (f(z)/z)?λ . Using this we shall determine the coefficient estimate for inverses of functions in the classes \(\mathcal {S}^{*}(A,B)\) and Σ?(A,B). 相似文献
8.
Jia-Feng Tang 《Journal of Mathematical Analysis and Applications》2007,334(1):517-527
In this paper, we study the differential equations of the following form w2+R(z)2(w(k))=Q(z), where R(z), Q(z) are nonzero rational functions. We proved the following three conclusions: (1) If either P(z) or Q(z) is a nonconstant polynomial or k is an even integer, then the differential equation w2+P2(z)2(w(k))=Q(z) has no transcendental meromorphic solution; if P(z), Q(z) are constants and k is an odd integer, then the differential equation has only transcendental meromorphic solutions of the form f(z)=acos(bz+c). (2) If either P(z) or Q(z) is a nonconstant polynomial or k>1, then the differential equation w2+(z−z0)P2(z)2(w(k))=Q(z) has no transcendental meromorphic solution, furthermore the differential equation w2+A(z−z0)2(w′)=B, where A, B are nonzero constants, has only transcendental meromorphic solutions of the form , where a, b are constants such that Ab2=1, a2=B. (3) If the differential equation , where P is a nonconstant polynomial and Q is a nonzero rational function, has a transcendental meromorphic solution, then k is an odd integer and Q is a polynomial. Furthermore, if k=1, then Q(z)≡C (constant) and the solution is of the form f(z)=Bcosq(z), where B is a constant such that B2=C and q′(z)=±P(z). 相似文献
9.
10.
Boris Shekhtman 《Constructive Approximation》1992,8(3):371-377
We give a new presentation and various extensions of one theorem of Somorjai. For any sequence of operatorsL n , given byL n f=∑ k=1 n f(z n,k )l n,k withz n, k ∈T andl n, k ∈A(T), there exists a functionf∈A(T) such thatL n f does not converge tof. 相似文献
11.
Zong-Xuan Chen 《Journal of Mathematical Analysis and Applications》2011,373(1):235-241
In this paper, we study growth and zeros of linear difference equations
Pn(z)f(z+n)+?+P1(z)f(z+1)+P0(z)f(z)=F(z) 相似文献
13.
E.F. Clifford 《Journal of Mathematical Analysis and Applications》2005,312(1):195-204
We prove a value distribution result which has several interesting corollaries. Let k∈N, let α∈C and let f be a transcendental entire function with order less than 1/2. Then for every nonconstant entire function g, we have that (f○g)(k)−α has infinitely many zeros. This result also holds when k=1, for every transcendental entire function g. We also prove the following result for normal families. Let k∈N, let f be a transcendental entire function with ρ(f)<1/k, and let a0,…,ak−1,a be analytic functions in a domain Ω. Then the family of analytic functions g such that
14.
R. Nair 《Periodica Mathematica Hungarica》2012,64(1):39-51
Let S be a countable semigroup acting in a measure-preserving fashion (g ? T g ) on a measure space (Ω, A, µ). For a finite subset A of S, let |A| denote its cardinality. Let (A k ) k=1 ∞ be a sequence of subsets of S satisfying conditions related to those in the ergodic theorem for semi-group actions of A. A. Tempelman. For A-measureable functions f on the measure space (Ω, A, μ) we form for k ≥ 1 the Templeman averages \(\pi _k (f)(x) = \left| {A_k } \right|^{ - 1} \sum\nolimits_{g \in A_k } {T_g f(x)}\) and set V q f(x) = (Σ k≥1|π k+1(f)(x) ? π k (f)(x)|q)1/q when q ∈ (1, 2]. We show that there exists C > 0 such that for all f in L 1(Ω, A, µ) we have µ({x ∈ Ω: V q f(x) > λ}) ≤ C(∫Ω | f | dµ/λ). Finally, some concrete examples are constructed. 相似文献
15.
M. Obradovi? 《Journal of Mathematical Analysis and Applications》2007,336(2):758-767
Let U(λ) denote the class of all analytic functions f in the unit disk Δ of the form f(z)=z+a2z2+? satisfying the condition
16.
On a certain type of nonlinear differential equations admitting transcendental meromorphic solutions
We study the differential equations w 2+R(z)(w (k))2 = Q(z), where R(z),Q(z) are nonzero rational functions. We prove
- if the differential equation w 2+R(z)(w′)2 = Q(z), where R(z), Q(z) are nonzero rational functions, admits a transcendental meromorphic solution f, then Q ≡ C (constant), the multiplicities of the zeros of R(z) are no greater than 2 and f(z) = √C cos α(z), where α(z) is a primitive of $\tfrac{1} {{\sqrt {R(z)} }}$ such that √C cos α(z) is a transcendental meromorphic function.
- if the differential equation w 2 + R(z)(w (k))2 = Q(z), where k ? 2 is an integer and R,Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C (constant), R(z) ≡ A (constant) and f(z) = √C cos (az + b), where $a^{2k} = \tfrac{1} {A}$ .
17.
Anne Greenbaum 《Linear algebra and its applications》2009,430(1):52-2352
Given an n by n matrix A, we look for a set S in the complex plane and positive scalars m and M such that for all functions p bounded and analytic on S and throughout a neighborhood of each eigenvalue of A, the inequalities
m·inf{‖f‖L∞(S):f(A)=p(A)}?‖p(A)‖?M·inf{‖f‖L∞(S):f(A)=p(A)} 相似文献
18.
Qian Lu 《Journal of Mathematical Analysis and Applications》2008,340(1):394-400
We consider the normality criterion for a families F meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each z∈Δ, such that there not only exists a positive number ε0 such that |an(a(z)−1)−1|?ε0 for arbitrary sequence of integers an(n∈N) and for any z∈Δ, but also exists a positive number B>0 such that for every f(z)∈F, B|f′(z)|?|f(z)| whenever f(z)f″(z)−a(z)(f′2(z))=0 in Δ. Then is normal in Δ. 相似文献
19.
20.
A polynomial projector Π of degree d on is said to preserve homogeneous partial differential equations (HPDE) of degree k if for every and every homogeneous polynomial of degree k, q(z)=∑|α|=kaαzα, there holds the implication: q(D)f=0q(D)Π(f)=0. We prove that a polynomial projector Π preserves HPDE of degree if and only if there are analytic functionals with such that Π is represented in the following form with some , where uα(z)zα/α!. Moreover, we give an example of polynomial projectors preserving HPDE of degree k (k1) without preserving HPDE of smaller degree. We also give a characterization of Abel–Gontcharoff projectors as the only Birkhoff polynomial projectors that preserve all HPDE. 相似文献