(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 **convolution** **operators** 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

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By using the technique of Herz-type Hardy spaces for the Dunkl operator Λα , we are attempting in this paper to study the Dunkl convolution operators, and we establish a version of multi[r]

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In , Godefroy and Shapiro [] showed that every continuous linear operator L : H(C) → H(C) which commutes with translations (these **operators** are called **convolution** **operators**) 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 **convolution** **operators** 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

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[3] 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. [4] J. Dziok and H. M. Srivastava. Classes of analytic functions associated with the general-

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I n this paper, we analyse Composite **Convolution** **operators** which are obtained by composing **convolution** **operators** with composition **operators**. We calculate the norm of composite **convolution** **operators**. The norm of trace of composite **convolution** **operators** 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 **convolution** **operators**. 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 [7] is the first to explicitly demonstrate some of the difficulties of using unstable linear **convolution** **operators** in full time axis stabilization studies (a brief discussion appears in [8]). In fact, the literature contains numerous erroneous treat- ments of such problems as discussed in [18]. Reference [21] 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 **convolution** **operators** for linear normed spaces of equivalence classes of signals obtained from interesting linear seminormed spaces of persistent signals on .

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3. **Convolution** conditions. In [7], Silverman, Silvia, and Telage considered some **convolution** conditions for starlikeness of analytic functions. Recently, Silverman and Silvia [6] 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 **convolution** **operators** for meromorphic functions to be in p ∗ (α) and ᐀ n+p−1 (α).

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Moreover, **convolution**-diﬀerential equations (CDEs) have been treated, e.g., in [, – ] and []. **Convolution** **operators** 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

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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 **convolution** **operators** 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.

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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 **convolution** **operators** 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, **convolution** **operators**.

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.

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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 [1], 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.

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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 .

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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.

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Let h be any convex univalent analytic function on U with.. It is proved in this paper that the class.[r]

The sine integral Siλx and the cosine integral Ciλx and their associated functions Si+ λx, Si− λx, Ci+ λx, Ci− λx are defined as locally summable functions on the real line.. Some convol[r]

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Adem Kılıçman: Department of Mathematics, University of Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia Current address: Institute of Advanced Technology, University of Putra Mala[r]

Recall that most of the convolutions like Dirichlet’s convolution, Uni- tary convolution and k -free convolution induce meet semi lattice structure on Z + [9].. For this reason we consid[r]