Nonclassical convolutions and their uses

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Ivan Dimovski
Keyword(s):  
Differentiation Operator ◽  
Linear Functionals ◽  
Direct Construction ◽  
Euler Operator

AbstractA survey of three types of convolutions, depending on arbitrary linear functionals is made. They are convolutions for right inverse operators of the differentiation operator, the Euler operator and the square of the differentiation operator. Three lines of applications of these convolutions are outlined: characterizing their multipliers, the commutants and direct construction of operational calculi.

Direct Construction and Screening of the Expression Vector of Anaerobic Clostridium in Escherichia coli

2013 ◽  
Vol 19 (5) ◽  
pp. 822-826
Author(s):  
Chunyu LIU ◽  
Yan CHEN ◽  
Jinqun HUANG ◽  
Jianxin PEI ◽  
Hao PANG ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Expression Vector ◽  
Direct Construction

On a Discrete-Time System Expressed in the Euler Operator

1988 ◽  
Author(s):  
Noriyuki Hori ◽  
Peter N. Nikiforuk ◽  
Kimio Kanai
Keyword(s):  
Discrete Time ◽  
Discrete Time System ◽  
Time System ◽  
Euler Operator

Bounded Linear Functionals on L q

1965 ◽  
Vol 72 (7) ◽  
pp. 750
Author(s):  
W. Fulks
Keyword(s):  
Linear Functionals ◽  
Bounded Linear

scholarly journals Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Gabriel G. Plunk ◽  
Matt Landreman ◽  
Per Helander
Keyword(s):  
Numerical Method ◽  
Plasma Phys ◽  
Magnetic Axis ◽  
Direct Construction ◽  
Numerical Construction ◽  
First Order

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren & Boozer (Phys. Fluids B, vol. 3 (10), 1991a, pp. 2805–2821). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman & Sengupta (J. Plasma Phys., vol. 84 (6), 2018, 905840616); Landreman et al. (J. Plasma Phys., vol. 85 (1), 2019, 905850103), enables their efficient numerical construction.

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

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