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

Ting-Bin Cao; Zhong-Shu Deng

Displaying similar documents to “Solutions of non-homogeneous linear differential equations in the unit disc”

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

Similarity:

Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

Similarity:

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

Similarity:

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 ${\tilde{R}}^{λ} (a, c, A, B)$ 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.

Zeros of functions in $D^{p, α}$ spaces

M. Jevtić (1981)

Matematički Vesnik

Similarity:

Properties of functions concerned with Caratheodory functions

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

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let $𝒫_{n}$ denote the class of analytic functions $p (z)$ of the form $p (z) = 1 + c_{n} z^{n} + c_{n + 1} z^{n + 1} + \dots$ 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

Similarity:

We prove that any divisor $Y$ of a global analytic set $X \subset ℝ^{n}$ 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 $H_{q - 1}^{\infty} (X, ℤ_{2})$ then the divisor $Y$ is globally principal.

Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

R. M. El-Ashwah, M. K. Aouf, S. M. El-Deeb (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this paper we introduce and investigate three new subclasses of $p$ -valent analytic functions by using the linear operator $D_{λ, p}^{m} (f * g) (z)$ . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for $(n, θ)$ -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

M. K. Aouf, A. Shamandy, A. O. Mostafa, S. M. Madian (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let $A$ denote the class of analytic functions with the normalization $f (0) = f^{'} (0) - 1 = 0$ in the open unit disc $U = {z : |z| < 1}$ . Set $f_{λ}^{n} (z) = z + \sum_{k = 2}^{\infty} {[1 + λ (k - 1)]}^{n} z^{k} (n \in N_{0}; λ \geq 0; z \in U),$ and define $f_{λ, μ}^{n}$ in terms of the Hadamard product $f_{λ}^{n} (z) * f_{λ, μ}^{n} = \frac{z}{{(1 - z)}^{μ}} (μ > 0; z \in U) .$ In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_{λ, μ}^{n} : A ⟶ A$ , given by $I_{λ, μ}^{n} f (z) = f_{λ, μ}^{n} (z) * f (z) (f \in A; n \in N_{0;} λ \geq 0; μ > 0) .$ Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Local analytic solutions of the functional equation $Φ (z) = H (z; Φ [f_{1} (z)], . . ., Φ [f_{m} (z)])$

Wilhelmina Smajdor (1970)

Annales Polonici Mathematici

Similarity:

The analytic $α$ -capacity and the Cauchy integral

K. Adžievski (1986)

Matematički Vesnik

Similarity:

Some new inhomogeneous Triebel-Lizorkin spaces on metric measure spaces and their various characterizations

Dachun Yang (2005)

Studia Mathematica

Similarity:

Let ${(X, ϱ, μ)}_{d, θ}$ be a space of homogeneous type, i.e. X is a set, ϱ is a quasi-metric on X with the property that there are constants θ ∈ (0,1] and C₀ > 0 such that for all x,x’,y ∈ X, $| ϱ (x, y) - ϱ (x^{'}, y) | \leq C ₀ ϱ {(x, x^{'})}^{θ} {[ϱ (x, y) + ϱ (x^{'}, y)]}^{1 - θ}$ , and μ is a nonnegative Borel regular measure on X such that for some d > 0 and all x ∈ X, $μ (y \in X : ϱ (x, y) < r) \sim r^{d}$ . Let ε ∈ (0,θ], |s| < ε and maxd/(d+ε),d/(d+s+ε) < q ≤ ∞. The author introduces new inhomogeneous Triebel-Lizorkin spaces $F_{\infty q}^{s} (X)$ and establishes their frame characterizations by first establishing a Plancherel-Pólya-type...

On Pólya's Theorem in several complex variables

Ozan Günyüz, Vyacheslav Zakharyuta (2015)

Banach Center Publications

Similarity:

Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{- k - 1}$ 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 $l i m s u p_{s \to \infty} {| H_{s} (f) |}^{1 / s ²} \leq d (K)$ , 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.

On the rigidity of webs

Michel Belliart (2007)

Bulletin de la Société Mathématique de France

Similarity:

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, $d \geq 3$ are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable $d$ -webs, however, there always exists a nonmeasurable conjugacy;...

Algebraic and analytic properties of solutions of abstract differential equations

R. Bittner

Similarity:

CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................

On convergence sets of divergent power series

Buma L. Fridman, Daowei Ma, Tejinder S. Neelon (2012)

Annales Polonici Mathematici

Similarity:

A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh [J. Reine Angew. Math. 241 (1970)], is introduced. Given a family $y = φ_{s} (t, x) = s b ₁ (x) t + b ₂ (x) t ² + \dots$ of analytic curves in ℂ × ℂⁿ passing through the origin, $C o n v_{φ} (f)$ of a formal power series f(y,t,x) ∈ ℂ[[y,t,x]] is defined to be the set of all s ∈ ℂ for which the power series $f (φ_{s} (t, x), t, x)$ converges as a series in (t,x). We prove that for a subset E ⊂ ℂ there exists a divergent formal power series f(y,t,x) ∈ ℂ[[y,t,x]] such that $E = C o n v_{φ} (f)$ if...

Relations between the boundary values and periods for generalized analytic functions in $R^{n}$

Wolfgang Tutschke (1983)

Banach Center Publications

Similarity:

On Hattori spaces

A. Bouziad, E. Sukhacheva (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a subset $A$ of the real line $ℝ$ , Hattori space $H (A)$ is a topological space whose underlying point set is the reals $ℝ$ 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...

Complements of analytic subvarieties and q-complete spaces

Edoardo Ballico (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Si dimostra che il complementare $X\setminus Y$ di un sottospazio analitico chiuso localmente intersezione completa di codimensione $q$ di una varietà di Stein è $q$ -completo.

Analytic aspects of the circulant Hadamard conjecture

Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)

Annales mathématiques Blaise Pascal

Similarity:

We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $| q_{0} | = ... = | q_{N - 1} | = 1$ the quantity $Φ = \sum_{i + k = j + l} \frac{q_{i} q_{k}}{q_{j} q_{l}}$ satisfies $Φ \geq N^{2}$ , with equality if and only if $q = (q_{i})$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $Φ$ , (2) the study of the critical points of $Φ$ , and (3) the computation of the moments of $Φ$ . We explore here...

Complete pluripolar graphs in $ℂ^{N}$

Nguyen Quang Dieu, Phung Van Manh (2014)

Annales Polonici Mathematici

Similarity:

Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that $Γ_{g} (F) : = (z, g (z)) : z \in F$ is complete pluripolar in $ℂ^{N + 1}$ . Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that $Γ_{g} (D)$ is complete pluripolar in $ℂ^{N + 1}$ . These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math....

Twists and resonance of $L$ -functions, I

Jerzy Kaczorowski, Alberto Perelli (2016)

Journal of the European Mathematical Society

Similarity:

We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents $\leq 1 / d$ of the $L$ -functions of any degree $d \geq 1$ in the extended Selberg class. In particular, this solves the resonance problem in all such cases.