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- W4286560482 abstract "We use the invariance of the triangle <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper T squared equals left-brace left-parenthesis x comma y right-parenthesis element-of double-struck upper R squared colon 0 less-than-or-slanted-equals x comma y comma 1 minus x minus y right-brace> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>T</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>:</mml:mo> <mml:mspace width=thinmathspace /> <mml:mn>0</mml:mn> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>,</mml:mo> <mml:mspace width=thinmathspace /> <mml:mn>1</mml:mn> <mml:mo>−<!-- − --></mml:mo> <mml:mi>x</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>y</mml:mi> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbf {T}^2={(x,y)in mathbb {R}^2:, 0leqslant x,y,, 1-x-y}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> under the permutations of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartSet x comma y comma 1 minus x minus y EndSet> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−<!-- − --></mml:mo> <mml:mi>x</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>y</mml:mi> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{x,y,1-x-y}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to construct and study two-variable orthogonal polynomial systems with respect to several distinct Sobolev inner products defined on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper T squared> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>T</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>mathbf {T}^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. These orthogonal polynomials can be constructed from two sequences of univariate orthogonal polynomials. In particular, one of the two univariate sequences of polynomials is orthogonal with respect to a Sobolev inner product and the other is a sequence of classical Jacobi polynomials." @default.
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- W4286560482 date "2022-07-22" @default.
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- W4286560482 title "On Sobolev orthogonal polynomials on a triangle" @default.
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