Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk
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DOI: 10.1007/s00010-016-0452-9
Abstract: Möbius addition is defined on the complex open unit disk by $$\begin{aligned} a\oplus _M b = \dfrac{a+b}{1+\bar{a}b} \end{aligned}$$a⊕Mb=a+b1+a¯band Möbius’s exponential equation takes the form $$L(a\oplus _M b) = L(a)L(b)$$L(a⊕Mb)=L(a)L(b), where L is a complex-valued function… read more here.
Keywords: equation; complex unit; unit disk; exponential equation ... See more keywords
Extremals for a Trudinger-Moser Inequality with a Vanishing Weight in the Unit Disk
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DOI: 10.1007/s10476-020-0049-3
Abstract: In this paper, we study a Trudinger-Moser inequality with a vanishing weight in the unit disk. Precisely, let $$B$$ B be the unit disk and β ≥ 0 be a real number. Denote $${\cal S}… read more here.
Keywords: unit disk; unit; inequality vanishing; moser inequality ... See more keywords
Multiple Interpolation and Principal Parts of a Laurent Series for Meromorphic Functions in the Unit Disk with Power Growth of the Nevanlinna Characteristic
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DOI: 10.1007/s11785-016-0592-x
Abstract: In this paper we solve the multiple interpolation problem in the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic under the condition that interpolation nodes are contained in… read more here.
Keywords: unit disk; functions unit; multiple interpolation; disk power ... See more keywords
Zeros of holomorphic functions in the unit disk and $$\rho $$ρ-trigonometrically convex functions
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DOI: 10.1007/s13324-019-00282-1
Abstract: Let M be a subharmonic function with Riesz measure $$\mu _M$$μM on the unit disk $${\mathbb {D}}$$D in the complex plane $${\mathbb {C}}$$C. Let f be a nonzero holomorphic function on $${\mathbb {D}}$$D such that… read more here.
Keywords: trigonometrically convex; rho trigonometrically; unit disk; convex functions ... See more keywords
Composition operators with a minimal commutant
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DOI: 10.1016/j.aim.2018.02.012
Abstract: Abstract Let C φ be a composition operator on the Hardy space H 2 , induced by a linear fractional self-map φ of the unit disk. We consider the question whether the commutant of C… read more here.
Keywords: minimal commutant; unit disk; map; self ... See more keywords
The Bohr-type operator on analytic functions and sections
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DOI: 10.1080/17476933.2021.1990272
Abstract: In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions f(z) = ∑ ∞ n=0 anz n in the unit disk. Later, we establish the Bohr-type operator on… read more here.
Keywords: bohr; unit disk; bohr type; analytic functions ... See more keywords
Note on the uniqueness holomorphic function on the unit disk
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DOI: 10.2298/fil1806321a
Abstract: Let f be an holomorphic function the unit disk to itself. We provide conditions on the local behavior of f along boundary near a finite set of the boundary points that requires f to be… read more here.
Keywords: function unit; unit disk; holomorphic function;
Lacunary Möbius Fractals on the Unit Disk
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DOI: 10.3390/sym13010091
Abstract: Centered polygonal lacunary functions are a type of lacunary function that exhibit behaviors that set them apart from other lacunary functions, this includes rotational symmetry. This work will build off of earlier studies to incorporate… read more here.
Keywords: lacunary bius; unit disk; unit; bius fractals ... See more keywords
New classes of spaceable sets of analytic functions on the open unit disk
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DOI: 10.4064/cm8463-7-2021
Abstract: In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined… read more here.
Keywords: open unit; unit disk; classes spaceable; analytic functions ... See more keywords