Displaying similar documents to “A Hankel matrix acting on Hardy and Bergman spaces”

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.

Area differences under analytic maps and operators

Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw (2024)

Czechoslovak Mathematical Journal

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Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of z h , we study various L 2 norms for T ϕ ( h ) , where T ϕ is the Toeplitz operator with symbol ϕ . In Theorem , given polynomials p and q we find a symbol ϕ such that T ϕ ( p ) = q . We extend some of our results to the polydisc.

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 )...

The generalized Toeplitz operators on the Fock space F α 2

Chunxu Xu, Tao Yu (2024)

Czechoslovak Mathematical Journal

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Let μ be a positive Borel measure on the complex plane n and let j = ( j 1 , , j n ) with j i . We study the generalized Toeplitz operators T μ ( j ) on the Fock space F α 2 . We prove that T μ ( j ) is bounded (or compact) on F α 2 if and only if μ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for T μ ( j ) to be in the Schatten p -class for 1 p < .

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.

Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Imed Feki, Ameni Massoudi (2024)

Czechoslovak Mathematical Journal

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We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces H k , p ( G ) , where k * , 1 p and G is either the open unit disk 𝔻 or the annular domain G s , 0 < s < 1 of the complex space . More precisely, we study the behavior on the interior of G of any function f belonging to the unit ball of the Hardy-Sobolev spaces H k , p ( G ) from its behavior on any open connected subset I of the boundary G of G with respect to the L 1 -norm. Our results can be viewed as an improvement and generalization of...

Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra

Ján Plavka (2016)

Kybernetika

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A vector x is said to be an eigenvector of a square max-min matrix A if A x = x . An eigenvector x of A is called the greatest 𝐗 -eigenvector of A if x 𝐗 = { x ; x ̲ x x ¯ } and y x for each eigenvector y 𝐗 . A max-min matrix A is called strongly 𝐗 -robust if the orbit x , A x , A 2 x , reaches the greatest 𝐗 -eigenvector with any starting vector of 𝐗 . We suggest an O ( n 3 ) algorithm for computing the greatest 𝐗 -eigenvector of A and study the strong 𝐗 -robustness. The necessary and sufficient conditions for strong 𝐗 -robustness are introduced...

( m , r ) -central Riordan arrays and their applications

Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He (2017)

Czechoslovak Mathematical Journal

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For integers m > r 0 , Brietzke (2008) defined the ( m , r ) -central coefficients of an infinite lower triangular matrix G = ( d , h ) = ( d n , k ) n , k as d m n + r , ( m - 1 ) n + r , with n = 0 , 1 , 2 , , and the ( m , r ) -central coefficient triangle of G as G ( m , r ) = ( d m n + r , ( m - 1 ) n + k + r ) n , k . It is known that the ( m , r ) -central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = ( d , h ) with h ( 0 ) = 0 and d ( 0 ) , h ' ( 0 ) 0 , we obtain the generating function of its ( m , r ) -central coefficients and give an explicit representation for the ( m , r ) -central Riordan array G ( m , r ) in terms of the Riordan array G ....

Distance matrices perturbed by Laplacians

Balaji Ramamurthy, Ravindra Bhalchandra Bapat, Shivani Goel (2020)

Applications of Mathematics

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Let T be a tree with n vertices. To each edge of T we assign a weight which is a positive definite matrix of some fixed order, say, s . Let D i j denote the sum of all the weights lying in the path connecting the vertices i and j of T . We now say that D i j is the distance between i and j . Define D : = [ D i j ] , where D i i is the s × s null matrix and for i j , D i j is the distance between i and j . Let G be an arbitrary connected weighted graph with n vertices, where each weight is a positive definite matrix of order...

Schatten class generalized Toeplitz operators on the Bergman space

Chunxu Xu, Tao Yu (2021)

Czechoslovak Mathematical Journal

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Let μ be a finite positive measure on the unit disk and let j 1 be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator T μ ( j ) to be bounded or compact. We first give a necessary and sufficient condition for T μ ( j ) to be in the Schatten p -class for 1 p < on the Bergman space A 2 , and then give a sufficient condition for T μ ( j ) to be in the Schatten p -class ( 0 < p < 1 ) on A 2 . We also discuss the generalized Toeplitz operators with general bounded symbols. If ϕ L ( D , d A ) and 1 < p < , we define the generalized...

( 0 , 1 ) -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

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Let m and n be positive integers, and let R = ( r 1 , ... , r m ) and S = ( s 1 , ... , s n ) be nonnegative integral vectors. Let A ( R , S ) be the set of all m × n ( 0 , 1 ) -matrices with row sum vector R and column vector S . Let R and S be nonincreasing, and let F ( R ) be the m × n ( 0 , 1 ) -matrix, where for each i , the i th row of F ( R , S ) consists of r i 1’s followed by ( n - r i ) 0’s. Let A A ( R , S ) . The discrepancy of A, disc ( A ) , is the number of positions in which F ( R ) has a 1 and A has a 0. In this paper we investigate linear operators mapping m × n matrices over...