9 problems

Consider a non-commutative quantum field theory formulated in terms of tempered ultrahyperfunctions, and let $\tilde\star$ denote the concrete type of star-product used in the form…

In a non-commutative quantum field theory, let ${\mathfrak W}^\star_m$ denote the Wightman functions involving the $\star$-product. Tempered-ultrahyperfunction characterization con…

Let $d4d0^{\bar{\otimes}N}$ be the covariant algebra of functions of $N$ points on lightlike $d4d0$-Minkowski space, and consider the free $d4d0$-Klein--Gordon theory whose two-poi…

Critical-index divergence conjecture. For the exact solution of the master equation, the critical index $n^{\mathcal{S}}$ diverges for

Stieltjes-property conjecture. The function $a\mapsto G_{aa}$ is a Stieltjes function for

Critical-slope conjecture. For every $\lambda>0$, there is a critical value of $a$ at which the slope of $\log(1+a)\mapsto\log G_{aa}$ decreases by $1$.

Banach fixed-point conjecture. The operator $\tilde{T}$ satisfies the assumptions of the Banach fixed-point theorem.

Stieltjes-equivalence conjecture. The function $a\to G_{aa}$ is Stieltjes if and only if the function $b\to G_{0b}$ is Stieltjes.

Stieltjes-function conjecture. The functions $G_{0b}$ and $G_{aa}$ are Stieltjes functions.