J. Korean Math. Soc. 2005; 42(3): 599-619
Printed May 1, 2005
Copyright © The Korean Mathematical Society.
Kwang Whoi Kim
JeonJu University
We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\Bbb C^n$ which are estimated with a special exponential function $\exp(\mu|x|)$.
Keywords: Fourier hyperfunction, convolution, convolution operator, convolutor, pseudodifferential operator, multiplier
MSC numbers: 46F15
2021; 58(5): 1147-1180
2014; 51(3): 567-592
1996; 33(3): 601-607
1996; 33(4): 929-954
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd