17 problems

The conjecture. If $u\in\mathcal G(\mathbb R^d)$ is weakly homogeneous of degree $\alpha$, then there is a representative $(u_\varepsilon)_\varepsilon$ of $u$ such that, for every…

Generalized complex analyticity conjecture. The authors conjecture that their generalized hyperfunctions are generalized complex analytic functions.

Let the $\Omega^{\prime}$-process solution be obtained by taking partial expectations in $\Omega$ of the multiplicative functionals associated to the $DB2^{\prime}$-process. The co…

Generality conjecture. The hyperfinite Fourier transform is very general.

Hyper-analyticity conjecture. This embedding yields hyper-analytic generalized smooth functions.

Let $M$ be the underlying manifold, let $U^i$ be smooth in $A'$, let $T^{\mu\ldots}_{\nu\ldots}\in D'^{m}_{n(A' o)}(M)$ admit an associated field $A_s(T^{\mu\ldots}_{\nu\ldots})$,…

Let $M$ be the underlying manifold, let $U^i$ be a piecewise smooth tensor field, let the connection belong to $\Gamma^{3}_{S}(M)$, and let…

Let $U^i$ be a piecewise smooth vector field and let $\Gamma^{\mu}_{\nu\alpha}\in\Gamma^{3}_{S}(M)$. Piecewise-smooth covariant-derivative conjecture. Covariant differentiation alo…

Let $M$ be a four-dimensional manifold, let $U^i$ be a vector field that is piecewise smooth and bounded on every compact set in every chart, let…

Let $M$ be the underlying manifold, and let $C,D,F,B\in\Gamma^{m}_{A}(M)$ belong to the same indicated classes $\Gamma^{m}_{A(At(\tilde A))}(M)$. Assume that, for every relevant…

Let $M$ be the underlying manifold. Let $\Gamma^{m}_{(A' o)}(M)$ and $\Gamma^{n}_{S}(M)$ be the indicated classes, and let $A_s$ denote the association map. Association–tensor-prod…

Let $M$ be the underlying manifold, and let $D'^{m}_{n (A' o)}(M)$ be the indicated class of tensor distributions. An associated field means the field associated to such an object…

Let $M$ be the underlying manifold, and let $\tilde D'^{a}_{b E A}(M)$ and $\tilde D'^{m}_{n E A}(M)$ denote the indicated classes of generalized tensor distributions, while…

Let $(\mathcal M,g)$ be a generalized space-time satisfying the metric assumptions referred to as condition (setting2) and (setting6), where condition (setting6) guarantees existen…

Let $(\mathcal M,g)$ be a generalized space-time with a symmetric representative $(g_\varepsilon)_\varepsilon$, and let $\Sigma$ be a past-compact space-like hypersurface. For suff…

Let $(\mathcal M,g)$ be a generalized stationary space-time, and let $(g_\varepsilon)_\varepsilon$ be a symmetric representative of its metric. The representative conjecture. On re…

Nonexistence conjecture. There exists $u\in{\rm Gen}_{\mathscr{S}}(\mathbb{R}^d)$ such that