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Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

)|\leq C_{\alpha ,\beta }\,(1+|\xi |)^{m-|\alpha |}} for all x,ξ ∈Rn, all multiindices α,β, some constants Cα, β and some real number m, then P belongs to the...

\left|I\right|=k} . The summation convention does not directly apply to multiindices since the summation over lengths needs to be displayed explicitly, e...

all compact subsets K of R n {\displaystyle \mathbb {R} ^{n}} and all multiindices α, there is an N > 0 such that sup x ∈ K | ∂ | α | ( ∂ x 1 ) α 1 ⋯ (...

,} where a {\displaystyle a} and B {\displaystyle B} are multiindices. The family of seminorms defined by p a , b ( f ) = sup x | x a D b f...

^{l(\mathbf {i} )}\end{array}}\right.} The i {\displaystyle \mathbf {i} } are multiindices and u {\displaystyle u} is a string of length n {\displaystyle n} : subsequences...