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On the Inverse Ultrahyperbolic Klein-Gordon Kernel

Author

Listed:
  • Kamsing Nonlaopon

    (Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In this work, we define the ultrahyperbolic Klein-Gordon operator of order α on the function f by T α ( f ) = W α ∗ f , where α ∈ C , W α is the ultrahyperbolic Klein-Gordon kernel, the symbol ∗ denotes the convolution, and f ∈ S , S is the Schwartz space of functions. Our purpose of this work is to study the convolution of W α and obtain the operator L α = T α − 1 such that if T α ( f ) = φ , then L α φ = f .

Suggested Citation

  • Kamsing Nonlaopon, 2019. "On the Inverse Ultrahyperbolic Klein-Gordon Kernel," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:534-:d:238867
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    References listed on IDEAS

    as
    1. Amphon Liangprom & Kamsing Nonlaopon, 2011. "On the Convolution Equation Related to the Diamond Klein-Gordon Operator," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, October.
    2. Darunee Maneetus & Kamsing Nonlaopon, 2011. "On the Inversion of Bessel Ultrahyperbolic Kernel of Marcel Riesz," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, November.
    3. Chalermpon Bunpog, 2018. "Boundary Value Problem of the Operator ⊕ k Related to the Biharmonic Operator and the Diamond Operator," Mathematics, MDPI, vol. 6(7), pages 1-11, July.
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    1. Chalermpon Bunpog, 2018. "Boundary Value Problem of the Operator ⊕ k Related to the Biharmonic Operator and the Diamond Operator," Mathematics, MDPI, vol. 6(7), pages 1-11, July.

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