Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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AN OPERATOR VALUED FUNCTION SPACE INTEGRAL OF FUNCTIONALS INVOLVING DOUBLE INTEGRALS

  • Published : 1997.04.01
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Abstract

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.

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References

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