On an Involution in the Class of Non-negative Hermitian Matrix Measures on a Compact Interval

Abstract

AbstractWe study a particular involution in the class $${\mathcal {M}^\succcurlyeq _{q}({[\alpha ,\beta ]})}$$ M q ≽ ( [ α , β ] ) of all Non-negative Hermitian $${q\times q}$$ q × q  measures on a compact interval $${[\alpha ,\beta ]}$$ [ α , β ] of $$\mathbb {R}$$ R . Several connections to the matricial version of the Hausdorff moment problem on $${[\alpha ,\beta ]}$$ [ α , β ] are investigated in terms of $${[\alpha ,\beta ]}$$ [ α , β ] -Stieltjes transforms as well as in the language of matricial Hausdorff moment sequences and associated matricial canonical moments.