Compa(ct Linear Operators On Blilbert Space And Their Appication To Integral Equations

Perhap the most theory developed about eigenvalue, eigenve t rand exi ten frnoluti on of a certain operator equ ation i for matrix operator , but th fir t part t brncon idered apart from matrices are integral operators, since the cia ical form ul ation fromrnphy ics, chemistry, engineerin.g, stati stics are of thi nature and the tudy of an integralrnoperators gives birth to the modern functional analysi . And the mo t common problemrnin appli ed mathematic are diffe rential operators which are fruitful source of integralrnequat ions. Due to various advantages of having integral equation rather than di ffere nti alrnequation usually we would like to convert and formulate differential equation in tornintegral equ ation. Many of integral operators encountered in application are boundedrnoperators and many of them are, in fac t, in special classes of bounded operator calledrncompact operators and again the most important classes of compact are the HilbertSchmidtrnoperators.

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