An Orthogonal Series Expansions Method to Hedge and Price European-Type Options

2016 ◽  
Author(s):  
Ron Chan
Keyword(s):  
Orthogonal Series ◽  
Series Expansions

scholarly journals Eigenfunction expansion of generalized functions

1978 ◽  
Vol 72 ◽  
pp. 1-25 ◽  
Author(s):  
J. N. Pandey ◽  
R. S. Pathak
Keyword(s):  
Hilbert Space ◽  
Eigenfunction Expansion ◽  
Orthogonal Series ◽  
Integral Transforms ◽  
Generalized Functions ◽  
Series Expansions ◽  
Schwartz Distributions ◽  
Space Technique

Expansions of generalized functions have been investigated by many authors. Korevaar [11], Widlund [20], Giertz [8], Walter [19] developed procedures for expanding generalized functions of Korevaar [12], Temple [17], and Lighthill [13], Expansions of certain Schwartz distributions [15] into series of orthonormal functions were given by Zemanian [23] (see also Zemanian [24]) and thereby he extended a number of integral transforms to distributions. The method involved in his work is very much related to the Hilbert space technique and is of somewhat different character from those used in most of the works on integral transforms such as [24, chapters 1-8]. Other works that discuss orthogonal series expansions involving generalized functions are by Bouix [1, chapter 7], Braga and Schönberg [2], Gelfand and Shilov [7, vol. 3, chapter 4] and Warmbrod [21].

Autofocusing with the help of orthogonal series transforms

2010 ◽  
Vol 56 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Przemysław Śliwiński
Keyword(s):  
Trigonometric Polynomial ◽  
Orthogonal Series ◽  
Formal Analysis ◽  
Series Expansions ◽  
Digital Cameras ◽  
Generic Algorithm ◽  
Autofocus Algorithm ◽  
Wavelet Series

Autofocusing with the help of orthogonal series transformsAn autofocus algorithm employing orthogonal series expansions is proposed. Several instances of the generic algorithm, based on discrete trigonometric, polynomial and wavelet series, are reviewed. The algorithms are easy to implement in the transform coders used in digital cameras. Formal analysis of the algorithm properties is illustrated in experiments. Some practical issues are also discussed.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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