In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞...In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.展开更多
This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of ...This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.展开更多
We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the auth...We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.展开更多
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，...In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，α(0<p≤1,0<q, α<∞) into a given space are the same as those of A^p，α(0<p≤1, α>0) in almost every case considered. The corollaries on multipliers of the spaces A^p，q，α extend some related results.展开更多
We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under auto...We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.展开更多
Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition,...Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out.展开更多
文摘In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.
文摘This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.
文摘We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
文摘In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，α(0<p≤1,0<q, α<∞) into a given space are the same as those of A^p，α(0<p≤1, α>0) in almost every case considered. The corollaries on multipliers of the spaces A^p，q，α extend some related results.
基金partially supported by Spanish MINECO/FEDER PGC2018-094431-B-I00partially supported by the Academy of Finland Project 296718。
文摘We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.
基金supported by Cultivation Program for Oustanding Young Teachers of Guangdong Province (Grant No. Yq2014060)Macao Science Technology Fund (Grant No. FDCT/099/ 2014/A2)
文摘Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out.
