Compa(ct Linear Operators on Blilbert Space and their App[ication to Integral Equations
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Date
2011-01
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Addis Ababa,
Abstract
Perhap the most theory developed about eigenvalue, eigenve t rand exi ten f
oluti on of a certain operator equ ation i for matrix operator , but th fir t part t b
con idered apart from matrices are integral operators, since the cia ical form ul ation from
phy ics, chemistry, engineerin.g, stati stics are of thi nature and the tudy of an integral
operators gives birth to the modern functional analysi . And the mo t common problem
in appli ed mathematic are diffe rential operators which are fruitful source of integral
equat ions. Due to various advantages of having integral equation rather than di ffere nti al
equation usually we would like to convert and formulate differential equation in to
integral equ ation. Many of integral operators encountered in application are bounded
operators and many of them are, in fac t, in special classes of bounded operator called
compact operators and again the most important classes of compact are the HilbertSchmidt
operators.
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Compa(ct Linear Operators