DiracDelta[Subscript[x, 1], Subscript[x, 2], \[Ellipsis]] == 0 /; Element[Subscript[x, 1], Reals] && Element[Subscript[x, 2], Reals] && \[Ellipsis] && Subscript[x, 1]^2 + Subscript[x, 2]^2 + \[Ellipsis] != 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]"]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[SubscriptBox["x", "1"], "\[Element]", "Reals"]], "\[And]", RowBox[List[SubscriptBox["x", "2"], "\[Element]", "Reals"]], "\[And]", "\[Ellipsis]", "\[And]", RowBox[List[RowBox[List[SuperscriptBox[SubscriptBox["x", "1"], "2"], "+", SuperscriptBox[SubscriptBox["x", "2"], "2"], "+", "\[Ellipsis]"]], " ", "\[NotEqual]", "0"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mo> &#8230; </mo> <mo> &#8743; </mo> <mrow> <mrow> <msubsup> <mi> x </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> + </mo> <msubsup> <mi> x </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> DiracDelta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <reals /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <reals /> </apply> <ci> &#8230; </ci> <apply> <neq /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", "\[Ellipsis]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[SubscriptBox["x", "1"], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["x", "2"], "\[Element]", "Reals"]], "&&", "\[Ellipsis]", "&&", RowBox[List[RowBox[List[SubsuperscriptBox["x", "1", "2"], "+", SubsuperscriptBox["x", "2", "2"], "+", "\[Ellipsis]"]], "\[NotEqual]", "0"]]]]]]]]]]

2001-10-29