Matrix Integral Operators on a Finite Interval with Kernels Depending on the Difference of the Arguments

2010 ◽  
pp. 47-63
Author(s):  
Israel Gohberg ◽  
Georg Heinig
Keyword(s):  
Finite Interval ◽  
Integral Operators ◽  
Matrix Integral ◽  
The Difference

A generalized class of integral operators

2020 ◽  
Vol 36 (3) ◽  
pp. 423-431
Author(s):  
VIJAY GUPTA
Keyword(s):  
Large Class ◽  
Present Note ◽  
Integral Operators ◽  
Basis Functions ◽  
Unified Approach ◽  
Quantitative Estimates ◽  
Special Cases ◽  
Discrete Operators ◽  
Durrmeyer Type Operators ◽  
The Difference

We introduce in the present note a unified approach to define integral operators, which include many well-known operators viz. Durrmeyer type operators, mixed hybrid operators as special cases. We also obtain the quantitative estimates between the difference of such integral operators with the discrete operators having same and different basis functions. Our operators proposed here give a very large class of integral operators, which have been discussed and proposed by several researchers in past seven decades.

Carleman integral operators with kernels depending on the difference and sum of the arguments

1977 ◽  
Vol 18 (1) ◽  
pp. 1-15 ◽  
Author(s):  
E. L. Aleksandrov ◽  
B. I. Kirichenko
Keyword(s):  
Integral Operators ◽  
The Difference

Derivation of correction terms for general quadrature formulae

1969 ◽  
Vol 66 (3) ◽  
pp. 571-586 ◽  
Author(s):  
J. A. Grant
Keyword(s):  
Finite Interval ◽  
Bernoulli Polynomials ◽  
Type A ◽  
Weighted Sum ◽  
Type B ◽  
Quadrature Formulae ◽  
The Difference ◽  
Correction Terms

AbstractIn this paper, it will be shown how it is possible, using Bernoulli polynomials of the first kind, to derive correction terms for any quadrature approximation in the form of a weighted sum over a finite interval. The terms derived will involve either the difference or the sum of derivatives taken at the ends of the range of integration, and they will be described as being of either Type A or Type B respectively. There will also be some discussion of the uses of such terms.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

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