In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q...The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q]-order of solutions of the equation are obtained by using a notion of new[p,q]-type on coefficients.展开更多
This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)i...This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.展开更多
Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)i...Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.展开更多
In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equatio...In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.展开更多
In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on...In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)+1 种基金the Youth Science Foundation of Education Bureau of Jiangxi Province(Grant No.GJJ12207)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11861023,11501142)the Foundation of Science and Technology Project of Guizhou Province(Grant No.20185769-05)+1 种基金the Foundation of Doctoral Research Program of Guizhou Normal University 2016the Foundation of Science and Technology of Guizhou Province(Grant No.20152112)。
文摘The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q]-order of solutions of the equation are obtained by using a notion of new[p,q]-type on coefficients.
基金The Science and Technology Development Fund,Macao SAR(File no.0123/2018/A3)supported by the Natural Science Foundation of China(61961003,61561006,11501132)+2 种基金Natural Science Foundation of Guangxi(2016GXNSFAA380049)the talent project of the Education Department of the Guangxi Government for one thousand Young-Middle-Aged backbone teachersthe Natural Science Foundation of China(12071035)。
文摘This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.
基金supported by the National Natural Science Foundation of China(Grant No.11942109).
文摘Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.
文摘In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.
基金supported by the National Natural Science Foundation of China(11301233 and 11171119)the Natural Science Foundation of Jiangxi Province(20114BAB211003 and 20122BAB211005)
文摘In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.
