Let C be the unit circle {z: |z| = 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L_2[−1,1] is greater than 1/8
In this paper some inequalities for Dirichlet\u27s and Fejer\u27s kernels proved in [6] are refined ...
AbstractGiven n+1 angles 0≤θ0<θ1⋯<θn≤π, we discuss various extremal problems over the class of polyn...
AbstractLet D be the unit disk in the complex plane C. We prove that for any polynomial p of degree ...
AbstractIf p(z)=∑ν=0naνzν is a polynomial of degree n having all its zeros in |z|⩽k, k⩾1, then Govil...
We show that for many families of OPUC, one has ‖φ'_n‖2/n → l, a condition we call normal behavior. ...
AbstractA bivariable polynomial of total degree n that has minimal uniform norm on a disk is explici...
AbstractLet p(z)=a0+⋯+anzn and q(z)=b0+⋯ be polynomials of degree respectively n and less than n suc...
In this paper we prove that the condition $$sum_{k=left[frac{n}{2}right]}^{2n}frac{k^{r}lambda _{k}}...
AbstractA singular integral equation with a Holderian second member function on [a,b] is considered ...
AbstractWe consider a class of holomorphic nonvanishing functions f(z)=1+a1z+⋯ in the unit disk |z|<...
AbstractLet Pn be the class of all polynomials of degree at most n, and let Mp(g;ρ) denote the Lp me...
AbstractLet n>1 be an integer, f∈Cn[a,b], and A:C[a,b]→R a continuous linear functional which annihi...
Consider a unital Banach algebra A having the NC property: that 1 − A + 1 ⊆ A + 1 . Then | ...
We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreas...
AbstractLet p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for ea...
In this paper some inequalities for Dirichlet\u27s and Fejer\u27s kernels proved in [6] are refined ...
AbstractGiven n+1 angles 0≤θ0<θ1⋯<θn≤π, we discuss various extremal problems over the class of polyn...
AbstractLet D be the unit disk in the complex plane C. We prove that for any polynomial p of degree ...
AbstractIf p(z)=∑ν=0naνzν is a polynomial of degree n having all its zeros in |z|⩽k, k⩾1, then Govil...
We show that for many families of OPUC, one has ‖φ'_n‖2/n → l, a condition we call normal behavior. ...
AbstractA bivariable polynomial of total degree n that has minimal uniform norm on a disk is explici...
AbstractLet p(z)=a0+⋯+anzn and q(z)=b0+⋯ be polynomials of degree respectively n and less than n suc...
In this paper we prove that the condition $$sum_{k=left[frac{n}{2}right]}^{2n}frac{k^{r}lambda _{k}}...
AbstractA singular integral equation with a Holderian second member function on [a,b] is considered ...
AbstractWe consider a class of holomorphic nonvanishing functions f(z)=1+a1z+⋯ in the unit disk |z|<...
AbstractLet Pn be the class of all polynomials of degree at most n, and let Mp(g;ρ) denote the Lp me...
AbstractLet n>1 be an integer, f∈Cn[a,b], and A:C[a,b]→R a continuous linear functional which annihi...
Consider a unital Banach algebra A having the NC property: that 1 − A + 1 ⊆ A + 1 . Then | ...
We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreas...
AbstractLet p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for ea...
In this paper some inequalities for Dirichlet\u27s and Fejer\u27s kernels proved in [6] are refined ...
AbstractGiven n+1 angles 0≤θ0<θ1⋯<θn≤π, we discuss various extremal problems over the class of polyn...
AbstractLet D be the unit disk in the complex plane C. We prove that for any polynomial p of degree ...
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