Generalized polynomials of the best Lp-approximation subject to interpolatory constraints

1979 ◽  
pp. 292-300
Author(s):  
I. Maruşciac
Keyword(s):  
Generalized Polynomials ◽  
Lp Approximation

scholarly journals INVERSE THEOREM IN LP-APPROXIMATION BY MODIFIED SZÄSZ-MIRAKYAN OPERATORS

1995 ◽  
Vol 28 (2) ◽  
pp. 285-292
Author(s):  
Vijay Gupta ◽  
G. S. Srivastava ◽  
T. A. K Sinha
Keyword(s):  
Inverse Theorem ◽  
Lp Approximation

Exponential operators, generalized polynomials and evolution problems

2001 ◽  
Vol 61 (2) ◽  
pp. 99-108 ◽  
Author(s):  
G Dattoli ◽  
A.M Mancho ◽  
M Quattromini ◽  
A Torre
Keyword(s):  
Generalized Polynomials ◽  
Evolution Problems

Bernstein and Markov Type Inequalities for Generalized Non-Negative Polynomials

1991 ◽  
Vol 43 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Tamás Erdélyi
Keyword(s):  
Absolute Constant ◽  
Positive Real ◽  
Generalized Polynomials ◽  
Markov Type ◽  
Natural Way

AbstractGeneralized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be introduced in a natural way. Several inequalities holding for ordinary polynomials are expected to be true for generalized polynomials, by utilizing the generalized degree in place of the ordinary one. Based on Remez-type inequalities on the size of generalized polynomials, we establish Bernstein and Markov type inequalities for generalized non-negative polynomials, obtaining the best possible result up to a multiplicative absolute constant.

scholarly journals On the images of generalized polynomials evaluated on matrices over an algebraically closed skew field

2021 ◽  
Vol 610 ◽  
pp. 827-836
Author(s):  
Aria Beaupré ◽  
Emily Hoopes-Boyd ◽  
Grace O'Brien
Keyword(s):  
Generalized Polynomials ◽  
Skew Field

scholarly journals Free Function Theory Through Matrix Invariants

2017 ◽  
Vol 69 (02) ◽  
pp. 408-433 ◽  
Author(s):  
Igor Klep ◽  
Špela Špenko
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Function Theory ◽  
Rational Functions ◽  
Generalized Polynomials ◽  
Direct Sums ◽  
Real Analytic Functions ◽  
Power Series Expansions ◽  
Noncommutative Polynomials ◽  
Free Function

Abstract This paper concerns free function theory. Freemaps are free analogs of analytic functions in several complex variables and are defined in terms of freely noncommuting variables. A function of g noncommuting variables is a function on g-tuples of square matrices of all sizes that respects direct sums and simultaneous conjugation. Examples of such maps include noncommutative polynomials, noncommutative rational functions, and convergent noncommutative power series. In sharp contrast to the existing literature in free analysis, this article investigates free maps with involution, free analogs of real analytic functions. To get a grip on these, techniques and tools from invariant theory are developed and applied to free analysis. Here is a sample of the results obtained. A characterization of polynomial free maps via properties of their finite-dimensional slices is presented and then used to establish power series expansions for analytic free maps about scalar and non-scalar points; the latter are series of generalized polynomials for which an invarianttheoretic characterization is given. Furthermore, an inverse and implicit function theorem for free maps with involution is obtained. Finally, with a selection of carefully chosen examples it is shown that free maps with involution do not exhibit strong rigidity properties enjoyed by their involutionfree counterparts.

Lp-Approximation durch Splines mit freien Knoten

1987 ◽  
Vol 131 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Bernd Mulansky
Keyword(s):  
Lp Approximation
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