🚀 go-pugleaf

In article <KOUJI-T.96Jan16151434@alpha718.is.aist-nara.ac.jp> kouji-t@is.aist-nara.ac.jp (Norihisa Taoka) writes:

   +$B!g(B
   |  (1/x) e^{-ixy} dx
   -$B!g(B

   $B$N7W;;7k2L$,!"$I$&$J$k$+!"$o$+$kJ}$O!"$_$($J$$$G$7$g$&$+!)(B
     $B;d$HCN9g$$$,7W;;$7$?7k2L$G$O!"&P(Bi$B$K!"$J$C$?$N$G$9$,!"@5$7(B
   $B$$$G$7$g$&$+!)(B
     $B$b$7@5$7$$$H$9$k$H!"$3$l$O!"(B1/x$B$N%U!<%j%(JQ49$,Dj?t$K$J$k(B
   $B;v$rI=$7$^$9!#$7$+$7!"%U!<%j%(JQ49$K$h$C$FDj?t$HBP$K$J$k$N$O!"(B
   $B&D4X?t$@$HM}2r$7$F$$$^$9$N$G!"2?$+$*$+$7$/$J$$$G$7$g$&$+!)(B
     $B$D$^$j!"(B

   sqrt(2$B&P(B)$B&D(B(x)    $B"+!]!]!]!]"*(B  1 (constant)
   -sqrt(2/$B&P(B)i 1/x  $B"+!]!]!]!]"*(B  1 (constant)
		       FT, IFT                     

   $B$NN>J}$,@.$jN)$C$F$7$^$&$h$&$J5$$,$7$^$9!#%U!<%j%(JQ49$N#1BP(B
   $B#1$NBP1~$,Jx$l$F$7$^$&$H$$$&;v$G$7$g$&$+!)(B



$B$3$N$F$N(B $B$1$$$5$s(B $B$O(B $B$V$D$j$d(B $B$N(B $B$[$&$,(B $B$H$/$$(B :-)

1/x $B$O(B $B$2$s$F$s$G(B $B$H$/$$$;$$(B $B$,(B $B$"$k$N$G(B $B$=$N$^$^$G$O(B FT $B$,(B
ill-defined $B$G$9!#(B

well-defined $B$K(B $B$9$k$K$O!"$?$H$($P(B
   1/(x - i d ) 
(i = $B$-$g$9$&$?$s$$(B d = $B$S$7$g$&$j$g$&(B, d>0 )

$B$b$A$m$s(B 1/(x+id) $B$r$+$s$,$($k$P$"$$$b(B $B$"$j$^$9!#(B

$B$3$&$9$k$H!"$U$/$=$;$-$V$s$G$R$g$&$+$G$-$^$9$,!"$1$C$+$O!"(B

1/(x-id) => i \pi theta(-y)

$B$H$J$j$^$9!#(B
$B$3$3$G(B theta(t) $B$O(B t >0 $B$G(B 1, t<0 $B$G(B 0 $B$K$J$k$h$&$J(B $B$+$s$9$&(B
($B$+$$$@$s$+$s$9$&(B) $B$G$9!#(B

$B$G$9$+$i!"$&$($N(B $B$F$$$.$G(B $B$*$H$b$@$A$N(B $B$1$C$+$O(B y<0 $B$N$P$"$$$K(B
$B$?$@$7$$!#(B
$B$"$J$?$N(B $B$+$s$,$($O(B $B$?$7$+$K(B $B$?$@$7$$$o$1$G$9!#(B
$B$+$$$@$s$+$s$9$&(B $B$H(B $B$F$$$9$&(B $B$O$A$,$$$^$9$+$i!#(B

$B$J$*!"(B1/(x-id) $B$N(B $B$+$o$j$K(B 1/(x+id) $B$r$H$k$H(B $B$1$C$+$,(B $B$A$,$C$F$-$^$9!#(B
($B$G$9$+$i(B $B$d$O$j(B $B$?$s$K(B 1/x $B$N(B FT $B$H$$$C$?$P$"$$$O(B ill-defined)

-- 
Masaki OSHIKAWA		< oshikawa@physics.ubc.ca >
--------------------------------------------------------------------
Physics Department,             |   Phone: (604)822-1383
University of British Columbia  |   FAX  : (604)822-5324
6224 Agricultural Road,         |-----------------------------------
Vancouver BC V6T 1Z1 CANADA     | 

--
Masaki OSHIKAWA         < oshikawa@physics.ubc.ca >
--------------------------------------------------------------------
Physics Department,             |   Phone: (604)822-1383
University of British Columbia  |   FAX  : (604)822-5324
6224 Agricultural Road,         |-----------------------------------
Vancouver BC V6T 1Z1 CANADA     |