Displaying similar documents to “Zeros of functions in D p , α spaces”

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class R λ ( a , c , A , B ) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass R ˜ λ ( a , c , A , B ) of R λ ( a , c , A , B ) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

A Hankel matrix acting on Hardy and Bergman spaces

Petros Galanopoulos, José Ángel Peláez (2010)

Studia Mathematica

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Let μ be a finite positive Borel measure on [0,1). Let μ = ( μ n , k ) n , k 0 be the Hankel matrix with entries μ n , k = [ 0 , 1 ) t n + k d μ ( t ) . The matrix μ induces formally an operator on the space of all analytic functions in the unit disc by the fomula μ ( f ) ( z ) = n = 0 i ( k = 0 μ n , k a k ) z , z ∈ , where f ( z ) = n = 0 a z is an analytic function in . We characterize those positive Borel measures on [0,1) such that μ ( f ) ( z ) = [ 0 , 1 ) f ( t ) / ( 1 - t z ) d μ ( t ) for all f in the Hardy space H¹, and among them we describe those for which μ is bounded and compact on H¹. We also study the analogous problem for the Bergman space A². ...

Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang (2014)

Annales Polonici Mathematici

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Let A ζ = Ω - ρ ( ζ ) · Ω ¯ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K ζ ( z ) of A ζ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that A ζ is non-pseudoconvex when the dimension of A ζ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for ² l o g K ζ / ζ ζ ̅ , as well as its boundary behavior.

On Pólya's Theorem in several complex variables

Ozan Günyüz, Vyacheslav Zakharyuta (2015)

Banach Center Publications

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Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let f ( z ) = k = 0 a k z - k - 1 be its Taylor expansion at ∞, and H s ( f ) = d e t ( a k + l ) k , l = 0 s the sequence of Hankel determinants. The classical Pólya inequality says that l i m s u p s | H s ( f ) | 1 / s ² d ( K ) , where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya’s inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu, Cai-Feng Yi (2010)

Annales Polonici Mathematici

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We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + + a ( z ) f ' + D ( z ) f = 0 , (1) where D ( z ) = Q ( z ) e P ( z ) + Q ( z ) e P ( z ) + Q ( z ) e P ( z ) , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), a j ( z ) (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

Bounded evaluation operators from H p into q

Martin Smith (2007)

Studia Mathematica

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Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by T z , p ( f ) = ( 1 - | z | ² ) 1 / p f ( z ) . Necessary and sufficient conditions on zₙ are given such that T z , p maps the Hardy space H p boundedly into the sequence space q . A corresponding result for Bergman spaces is also stated.

Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + + a ( z ) f ' + a ( z ) f = F ( z ) , where all coefficients a , a , . . . , a k - 1 , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

Properties of functions concerned with Caratheodory functions

Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let 𝒫 n denote the class of analytic functions p ( z ) of the form p ( z ) = 1 + c n z n + c n + 1 z n + 1 + in the open unit disc 𝕌 . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for p ( z ) concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

Divisors in global analytic sets

Francesca Acquistapace, A. Díaz-Cano (2011)

Journal of the European Mathematical Society

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We prove that any divisor Y of a global analytic set X n has a generic equation, that is, there is an analytic function vanishing on Y with multiplicity one along each irreducible component of Y . We also prove that there are functions with arbitrary multiplicities along Y . The main result states that if X is pure dimensional, Y is locally principal, X / Y is not connected and Y represents the zero class in H q - 1 ( X , 2 ) then the divisor Y is globally principal.

Non supercyclic subsets of linear isometries on Banach spaces of analytic functions

Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari (2015)

Czechoslovak Mathematical Journal

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Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X . Sufficient conditions are given for non-supercyclicity of Γ . In particular, we show that the semigroup of linear isometries on the spaces S p ( p > 1 ), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H p or the Bergman space L a p ( 1 < p < , p 2 )...

Mobius invariant Besov spaces on the unit ball of n

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give new characterizations of the analytic Besov spaces B p on the unit ball 𝔹 of n in terms of oscillations and integral means over some Euclidian balls contained in 𝔹 .

Espace de Dixmier des opérateurs de Hankel sur les espaces de Bergman à poids

Romaric Tytgat (2015)

Czechoslovak Mathematical Journal

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Nous donnons des résultats théoriques sur l’idéal de Macaev et la trace de Dixmier. Ensuite, nous caractérisons les symboles antiholomorphes f ¯ tels que l’opérateur de Hankel H f ¯ sur l’espace de Bergman à poids soit dans l’idéal de Macaev et nous donnons la trace de Dixmier. Pour cela, nous regardons le comportement des normes de Schatten 𝒮 p quand p tend vers 1 et nous nous appuyons sur le résultat de Engliš et Rochberg sur l’espace de Bergman. Nous parlons aussi des puissances de tels opérateurs....

On the rigidity of webs

Michel Belliart (2007)

Bulletin de la Société Mathématique de France

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Plane d -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two d -webs, d 3 are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable d -webs, however, there always exists a nonmeasurable conjugacy;...

Linear maps preserving elements annihilated by the polynomial X Y - Y X

Jianlian Cui, Jinchuan Hou (2006)

Studia Mathematica

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Let H and K be complex complete indefinite inner product spaces, and ℬ(H,K) (ℬ(H) if K = H) the set of all bounded linear operators from H into K. For every T ∈ ℬ(H,K), denote by T the indefinite conjugate of T. Suppose that Φ: ℬ(H) → ℬ(K) is a bijective linear map. We prove that Φ satisfies Φ ( A ) Φ ( B ) = Φ ( B ) Φ ( A ) for all A, B ∈ ℬ(H) with A B = B A if and only if there exist a nonzero real number c and a generalized indefinite unitary operator U ∈ ℬ(H,K) such that Φ ( A ) = c U A U for all A ∈ ℬ(H).

Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions

Sunanda Naik, Karabi Rajbangshi (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator a , b by a , b ( f ) ( z ) = Γ ( a + 1 ) / Γ ( b + 1 ) 0 1 ( f ( t ) ( 1 - t ) b ) / ( ( 1 - t z ) a + 1 ) d t , where a and b are non-negative real numbers. In particular, for a = b = β, a , b becomes the generalized Hilbert operator β , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that a , b is bounded on Dirichlet-type spaces S p , 0 < p < 2, and on Bergman spaces A p , 2 < p < ∞. Also we find an upper bound for the norm of the operator a , b ....

On Hattori spaces

A. Bouziad, E. Sukhacheva (2017)

Commentationes Mathematicae Universitatis Carolinae

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For a subset A of the real line , Hattori space H ( A ) is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from A are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on A which are sufficient and necessary for H ( A ) to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...

A pure smoothness condition for Radó’s theorem for α -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

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Let Ω n be a bounded, simply connected -convex domain. Let α + n and let f be a function on Ω which is separately C 2 α j - 1 -smooth with respect to z j (by which we mean jointly C 2 α j - 1 -smooth with respect to Re z j , Im z j ). If f is α -analytic on Ω f - 1 ( 0 ) , then f is α -analytic on Ω . The result is well-known for the case α i = 1 , 1 i n , even when f a priori is only known to be continuous.

An integral operator on the classes 𝒮 * ( α ) and 𝒞𝒱ℋ ( β )

Nicoleta Ularu, Nicoleta Breaz (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class 𝒞𝒱ℋ ( β ) and also we estimate the first two coefficients for functions obtained by this operator applied on the class 𝒞𝒱ℋ ( β ) .