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1.
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   

2.
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
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3.
We prove regularity results for minimizers of functionals in the class , where is a fixed function and f is quasiconvex and fulfills a growth condition of the type
L−1|z|p(x)?f(x,ξ,z)?L(1+|z|p(x)),  相似文献   

4.
For j=1,…,n let fj(z) and gj(z) be holomorphic modular forms for such that fj(z)gj(z) is a cusp form. We define a series
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For the logarithmic coefficients γn of a univalent function f(z)=z+a2z2+?∈S, the well-known de Branges' theorem shows that
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In 2001, Borwein, Choi, and Yazdani looked at an extremal property of a class of polynomial with ±1 coefficients. Their key result was:
Theorem. (See Borwein, Choi, Yazdani, 2001.) Letf(z)=±z±z2±?±zN−1, and ζ a primitive Nth root of unity. If N is an odd positive integer then
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11.
Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,
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12.
Let F(z)=∑n=1a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
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13.
Let −(·,z)D+q be a differential operator in L2(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form
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For a complex number α with let be the class of analytic functions f in the unit disk with f(0)=0 satisfying in , for some convex univalent function in . For any fixed , and we shall determine the region of variability V(z0,α,λ) for f(z0) when f ranges over the class
In the final section we graphically illustrate the region of variability for several sets of parameters z0 and α.  相似文献   

17.
For γ?0 and β<1 given, let Pγ(β) denote the class of all analytic functions f in the unit disk with the normalization f(0)=f(0)−1=0 and satisfying the condition
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Given α>0 and fL2(0,1), we are interested in the equation
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20.
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for fL1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
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