(t, φ(t)) are said to be simple according to Drury and Marshall . The measure ω(t) dt supported on the curve (t, φ(t)) is known as the aﬃne arclength measure, which is based on the aﬃne arclength parameter as in , and was introduced by Drury and Marshall  in dealing with the Fourier restriction problem related to curves, and later by Drury  in studying convolutionoperators with measures supported on curves. We refer interested readers to [–] for the relevance of aﬃne geometry in this subject. One big beneﬁt of us- ing the aﬃne arclength measure in place of the Euclidean arclength measure + φ (t) dt
In , Godefroy and Shapiro  showed that every continuous linear operator L : H(C) → H(C) which commutes with translations (these operators are called convolutionoperators) and which is not a multiple of the identity is hypercyclic. This result uniﬁes two classical results by Birkhoﬀ and MacLane (see the survey ).
The study of operators plays a vital role in mathematics. To deﬁne an operator using the convolution theory, and then study its properties, is one of the hot areas of current ongoing research in the geometric function theory and its related ﬁelds. In this survey-type article, we discuss historic development and exploit the strengths and properties of some diﬀerential and integral convolutionoperators introduced and studied in the geometric function theory. It is hoped that this article will be beneﬁcial for the graduate students and researchers who intend to start work in this ﬁeld. MSC: 30C45; 30C50
 N. E. Cho, O. S. Kwon and H. M. Srivastava. Inclusion relationships and argument prop- erties for certain subclasses of multivalent functions associated with a family of linear operators. Journal of Mathematical Analysis and Applications, 292:470–483, 2004.  J. Dziok and H. M. Srivastava. Classes of analytic functions associated with the general-
I n this paper, we analyse Composite Convolutionoperators which are obtained by composing convolutionoperators with composition operators. We calculate the norm of composite convolutionoperators. The norm of trace of composite convolutionoperators has also been explored. In this paper, an attempt has been made to investigate semigroups of one-parameter family and two-parameter family of composite convolutionoperators. A dynamical system induced by composite convolution operator is also obtained.
Although various full-time axis control problems, and closed- loop identification problems, have been studied for a long time, it appears that  is the first to explicitly demonstrate some of the difficulties of using unstable linear convolutionoperators in full time axis stabilization studies (a brief discussion appears in ). In fact, the literature contains numerous erroneous treat- ments of such problems as discussed in . Reference  seems to be the first to demonstrate that the general linear I/O model , by allowing one to describe open-loop un- stable behavior without the need to introduce unbounded convo- lution operators, avoids many of the limitations of the basic I/O model in full time axis stabilization studies. We shall also provide a new type of argument concerning the limitations of unbounded convolutionoperators for linear normed spaces of equivalence classes of signals obtained from interesting linear seminormed spaces of persistent signals on .
3. Convolution conditions. In , Silverman, Silvia, and Telage considered some convolution conditions for starlikeness of analytic functions. Recently, Silverman and Silvia  showed many necessary and suﬃcient conditions in terms of convolution op- erators for an analytic function to be in classes of starlike and convex. In this section, we give some necessary and suﬃcient conditions in terms of convolutionoperators for meromorphic functions to be in p ∗ (α) and ᐀ n+p−1 (α).
Moreover, convolution-diﬀerential equations (CDEs) have been treated, e.g., in [, – ] and . Convolutionoperators in vector valued spaces are studied, e.g., in [–] and . However, the convolution-diﬀerential operator equations (CDOEs) are a rela- tively less investigated subject (see ). The main aim of the present paper is to establish the separability properties of the linear CDOE
T is replaced by the fractional integral operator; in [8, 9], these results on the Triebel- Lizorkin spaces and the case b ∈ Lip β (where Lip β is the homogeneous Lipschitz space) are obtained. The main purpose of this paper is to study the continuity of some multi- linear operators related to certain convolutionoperators on the Triebel-Lizorkin spaces. In fact, we will obtain the continuity on the Triebel-Lizorkin spaces for the multilinear operators only under certain conditions on the size of the operators. As the applications, the continuity of the multilinear operators related to the Littlewood-Paley operator and Marcinkiewicz operator on the Triebel-Lizorkin spaces are obtained.
results previously known for convolution estimates related to space curves, namely [1-6]. This article is organized as follows: in the following section, a uniform estimate for convolutionoperators with measures supported on plane curves. The proof of Theo- rem 1.1 based on a T*T method is given in Section 3.
Sibel Yal¸ cın received her Ph.D. degree in Mathematics in 2001 from Uludag Uni- versity, Bursa, Turkey. She became a full Professor in 2011. She is currently with the Department of Mathematics, Uludag University. Her research interests include harmonic mappings, geometric function theory, meromorphic functions, analytic func- tions, bi-univalent functions, convolutionoperators.
Oracle allows arithmetic operators to be used while viewing records from a table or while performing Data Manipulation operations such as insert, update and delete. You can use an arithmetic operator with one or two arguments to negate, add, subtract, multiply and divide numeric values. Some of these operators are also used in date time and interval arithmetic. The arguments to the operators must resolve to numeric data types or to any data types that can be implicitly converted to a numeric data types. Unary arithmetic operators return the same data type as the numeric data type of the arguments. For binary arithmetic operators, Oracle determines the arguments with the highest numeric precedence, implicitly converts the remaining arguments to that data type, and return that data type.
The typical approach for efficient convolution uses Fast Fourier Transforms (FFTs). While such implementations can be extremely efficient, there comes a limit where the increase in the number of points resulting from establishing a uniform grid – whether it is 10,000 or 100 million – outweighs the efficiency of the algorithm. While algorithms have been developed that utilize multiple grid/sampling rate resolutions , this is not a uniformly practical approach when working with measured data where there are potentially few, if any, portions of data that share a common spacing of RV values, or where algorithmically finding an appropriate grid might be more computationally intensive than doing the convolution calculation itself.
One of the most difficult parts after finding a pattern was finding a way to prove what I had found. The book I had been looking at worked with the column generating functions[KOS14]. Then I came across a journal article from Hoggat and Bicknell that found the convolution triangles in row generating functions[HB72]. Hoggat and Bicknell proved their finding in a different way, however, I believe I have made the process more simple. Let us start with a brief explanation of what we need in order to find the terms themselves. We need a way to write the rows so that we can find the individual terms. The way Hoggat and Bicknel[HB72] found it was through the function g(x) = (1−x) 1 n .
Few studies focus on the comprehensive pattern of ICT adoption among different types of adopter, i.e. older, new, high, and low adopter tour operators. The Diffusion of Innovation (DOI) curve, also known as adoption characteristics, has been used to identify the differences between the categories of adopters. The DOI curve consists of innovator, early adopter, early majority, late majority, and laggards. These categories represent the level of ICT adoption among tour operators. Hence, researchers that studied adoption characteristics (using the DOI Curve) used descriptive statistics to determine the patterns of different adopters (e.g. Jacobsen, 1998; Hashim, 2007; Keesee, 2010; Oliveira and Martins, 2011; Roy, 2018). Despite this, none of these studies examined the comprehensive relationship between all of the variables involved in this study. Consequently, after reviewing previous studies, a new conceptual framework was integrated and tested empirically including the proposed hypothesis in this study.