Dov Aharonov - Academia.edu (original) (raw)
Papers by Dov Aharonov
Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneo... more Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.
Complex Analysis and Operator Theory
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weak... more In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
J London Math Soc Second Ser, 1969
Transactions of the American Mathematical Society, 1994
The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that s"-> 0 as n-► oo. Rodin and Sul... more The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that s"-> 0 as n-► oo. Rodin and Sullivan conjectured that s" = 0(1/n). This has been proved by Z-Xu He [2]. Earlier, the present author proved the conjecture under some additional restrictions [1]. In the following we are able to remove these restrictions, and thus give an alternative proof of the RS conjecture. The proof is based on our previous article [1]. It is completely different from the proof of He, and it is mainly based on discrete potential theory, as developed by Rodin for the hexagonal case [4].
Canadian Journal of Mathematics, 1973
Canadian Mathematical Society. www.cms.math.ca. Go to CMS home page, Canadian Mathematical Societ... more Canadian Mathematical Society. www.cms.math.ca. Go to CMS home page, Canadian Mathematical Society. Social Media, |, Site map, |, CMS store. Membership: individual: benefits; categories; annual rates; join; renew; update your info; website accounts. institutional: benefits; categories & rates; join; renew. corporate; terms & conditions; membership lists: search; combined membership list (CML); individuals - alphabetic; individuals - geographic; individuals ...
Computational Methods and Function Theory, 2007
ABSTRACT Let S 0 be the standard class of non-vanishing univalent functions in the unit disc. In ... more ABSTRACT Let S 0 be the standard class of non-vanishing univalent functions in the unit disc. In this article we present a generalization of the classical ellipse theorem for this class.
Menahem Max Schiffer: Selected Papers Volume 2, 2013
Bulletin of the American Mathematical Society, 1970
Bulletin of the American Mathematical Society, 1969
Lecture Notes in Mathematics, 2000
One of the remarkable proofs of Milin is the elegant derivation of Hayman's regularity theor... more One of the remarkable proofs of Milin is the elegant derivation of Hayman's regularity theorem for the coefficients of univalent functions. Milin's proof [4] does not contain any integration. The main tool is the theorem of Bazilevič [2]. In the following we prove a stronger version of an important theorem of Hayman on the growth of univalent functions. Our proof is along Milin's approach. We also bring as an application a short proof of Hayman's regularity theorem [3] stating that | \tfraca n n | ®</font > a</font > = a</font >( f ) for any fe</font >s as n ®</font > ¥</font >.\left| {\tfrac{{^a n}}{{{\mathbf{ }}n}}} \right| \to \alpha = \alpha \left( f \right) for{\mathbf{ }}any{\mathbf{ }}f\varepsilon s{\mathbf{ }}as{\mathbf{ }}n \to \infty .
Isr J Math, 1970
ABSTRACT In the following we prove that for a given univalent function such that |a 2| a n |≦n fo... more ABSTRACT In the following we prove that for a given univalent function such that |a 2| a n |≦n for eachn. The method of proof is closely related to Milin’s method.
Journal of Mathematical Analysis and Applications, Apr 1, 2003
ABSTRACT In this chapter, we introduce the class of spirallike functions with respect to a bounda... more ABSTRACT In this chapter, we introduce the class of spirallike functions with respect to a boundary point. It turns out that, in fact, each such function is a complex power of a starlike function with respect to a boundary point. So, what we studied in the previous chapter forms the base for our present considerations. We start by looking at the images of spirallike functions with respect to a boundary point, i.e., spirallike domains, the boundary of which contains the origin.
This study began innocently enough with a search for extremal con gurations of circles in the Rod... more This study began innocently enough with a search for extremal con gurations of circles in the Rodin and Sullivan \Ring Lemma". This is an elementary geometric lemma which nevertheless plays a key role in recent work on circle packing and its connections to conformal mapping. However, the study evolved into something of a grand tour of various ideas bearing on the geometry of \quads" of circles as we discovered (and rediscovered) intertwining results stretching from antiquity right up to current work on residual sets of Kleinian groups. Our aim here is to share not only our results, but also some of the sights and surprises we encountered on this journey.
J Anal Math, 1993
Recently deBranges gave a very remarkable proof of Milin's conjecture. This implies both the conj... more Recently deBranges gave a very remarkable proof of Milin's conjecture. This implies both the conjectures of Robertson and Bieberbach. It is our aim to show that the statement of equality case in both Robertson's and Bierbach's conjectures may be proved by a different and easier method.
The article discusses criteria for univalence of analytic functions in the unit disc. A unified m... more The article discusses criteria for univalence of analytic functions in the unit disc. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.
The article discusses criteria for univalence of analytic functions in the unit disc. Various fam... more The article discusses criteria for univalence of analytic functions in the unit disc. Various families of analytic functions depending on real parameters are considered. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.
Illinois journal of mathematics
This paper is concerned with the relation between the regularity properties of a function and tho... more This paper is concerned with the relation between the regularity properties of a function and those of its variation function andwith some applications of these relations to some problems about harmonic functions. Before we state our results we recall some definitions and known facts.
Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneo... more Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.
Complex Analysis and Operator Theory
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weak... more In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
J London Math Soc Second Ser, 1969
Transactions of the American Mathematical Society, 1994
The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that s"-> 0 as n-► oo. Rodin and Sul... more The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that s"-> 0 as n-► oo. Rodin and Sullivan conjectured that s" = 0(1/n). This has been proved by Z-Xu He [2]. Earlier, the present author proved the conjecture under some additional restrictions [1]. In the following we are able to remove these restrictions, and thus give an alternative proof of the RS conjecture. The proof is based on our previous article [1]. It is completely different from the proof of He, and it is mainly based on discrete potential theory, as developed by Rodin for the hexagonal case [4].
Canadian Journal of Mathematics, 1973
Canadian Mathematical Society. www.cms.math.ca. Go to CMS home page, Canadian Mathematical Societ... more Canadian Mathematical Society. www.cms.math.ca. Go to CMS home page, Canadian Mathematical Society. Social Media, |, Site map, |, CMS store. Membership: individual: benefits; categories; annual rates; join; renew; update your info; website accounts. institutional: benefits; categories &amp; rates; join; renew. corporate; terms &amp; conditions; membership lists: search; combined membership list (CML); individuals - alphabetic; individuals - geographic; individuals ...
Computational Methods and Function Theory, 2007
ABSTRACT Let S 0 be the standard class of non-vanishing univalent functions in the unit disc. In ... more ABSTRACT Let S 0 be the standard class of non-vanishing univalent functions in the unit disc. In this article we present a generalization of the classical ellipse theorem for this class.
Menahem Max Schiffer: Selected Papers Volume 2, 2013
Bulletin of the American Mathematical Society, 1970
Bulletin of the American Mathematical Society, 1969
Lecture Notes in Mathematics, 2000
One of the remarkable proofs of Milin is the elegant derivation of Hayman's regularity theor... more One of the remarkable proofs of Milin is the elegant derivation of Hayman's regularity theorem for the coefficients of univalent functions. Milin's proof [4] does not contain any integration. The main tool is the theorem of Bazilevič [2]. In the following we prove a stronger version of an important theorem of Hayman on the growth of univalent functions. Our proof is along Milin's approach. We also bring as an application a short proof of Hayman's regularity theorem [3] stating that | \tfraca n n | ®</font > a</font > = a</font >( f ) for any fe</font >s as n ®</font > ¥</font >.\left| {\tfrac{{^a n}}{{{\mathbf{ }}n}}} \right| \to \alpha = \alpha \left( f \right) for{\mathbf{ }}any{\mathbf{ }}f\varepsilon s{\mathbf{ }}as{\mathbf{ }}n \to \infty .
Isr J Math, 1970
ABSTRACT In the following we prove that for a given univalent function such that |a 2| a n |≦n fo... more ABSTRACT In the following we prove that for a given univalent function such that |a 2| a n |≦n for eachn. The method of proof is closely related to Milin’s method.
Journal of Mathematical Analysis and Applications, Apr 1, 2003
ABSTRACT In this chapter, we introduce the class of spirallike functions with respect to a bounda... more ABSTRACT In this chapter, we introduce the class of spirallike functions with respect to a boundary point. It turns out that, in fact, each such function is a complex power of a starlike function with respect to a boundary point. So, what we studied in the previous chapter forms the base for our present considerations. We start by looking at the images of spirallike functions with respect to a boundary point, i.e., spirallike domains, the boundary of which contains the origin.
This study began innocently enough with a search for extremal con gurations of circles in the Rod... more This study began innocently enough with a search for extremal con gurations of circles in the Rodin and Sullivan \Ring Lemma". This is an elementary geometric lemma which nevertheless plays a key role in recent work on circle packing and its connections to conformal mapping. However, the study evolved into something of a grand tour of various ideas bearing on the geometry of \quads" of circles as we discovered (and rediscovered) intertwining results stretching from antiquity right up to current work on residual sets of Kleinian groups. Our aim here is to share not only our results, but also some of the sights and surprises we encountered on this journey.
J Anal Math, 1993
Recently deBranges gave a very remarkable proof of Milin's conjecture. This implies both the conj... more Recently deBranges gave a very remarkable proof of Milin's conjecture. This implies both the conjectures of Robertson and Bieberbach. It is our aim to show that the statement of equality case in both Robertson's and Bierbach's conjectures may be proved by a different and easier method.
The article discusses criteria for univalence of analytic functions in the unit disc. A unified m... more The article discusses criteria for univalence of analytic functions in the unit disc. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.
The article discusses criteria for univalence of analytic functions in the unit disc. Various fam... more The article discusses criteria for univalence of analytic functions in the unit disc. Various families of analytic functions depending on real parameters are considered. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.
Illinois journal of mathematics
This paper is concerned with the relation between the regularity properties of a function and tho... more This paper is concerned with the relation between the regularity properties of a function and those of its variation function andwith some applications of these relations to some problems about harmonic functions. Before we state our results we recall some definitions and known facts.