论文标题
BV空间和与Schrodinger运算符有关的外围，具有反方势和应用对等级定理的应用
BV spaces and the perimeters related to Schrodinger operators with inverse-square potentials and applications to the rank-one theorem
论文作者
论文摘要
对于$ a \ ge - {（\ frac {d} {2} -1）^2} $和$2σ= {d -2} - （{{{（d -2）}^2}^2} + 4a} + 4a}） \ frac {a} {{{{| x |}^2}}}}，\\ \ \ \ \ \ \ \\ widetilde {h}}_σ= 2 = 2 \ big（{ - δ+ \ frac {σ^2} {{{| x | x |}}}}}}}}}}}}}}}} \ big）潜力。在本文中，在域上$ω\ subset {\ Mathbb {r}^d} \ backslash \ {0 \ {0 \}，d \ geq 2，$％隔离，与原点相距甚远，$ {\ mathcal {\ mathcal {h} _a} _a} _a} _ BV space $ - bv space $ \ nathcal { _ {{\ Mathcal {h} _a}}}}}} $和$ {\ Mathcal {\ widetilde {\ widetilde {h}}_σ} $ - σ} $ - bv space $ \ Mathcal {bv space $ \ Mathcal {b} _σ}}}（ω）$分别引入了与$ \ mathcal {h} _ {a} $和$ \ Mathcal {\ widetilde {h}} _σ$有关的$。我们研究了$ \ Mathcal {b} {\ Mathcal {v} _ {{\ Mathcal {h} _a}}}}}}（ω）$和$ \ MATHCAL {b} {\ MATHCAL {\ MATHCAL {V} _ { _σ}}}（ω）$。此外，我们证明$ {\ Mathcal {\ widetilde {h}}_σ} $ - 可以通过其子图等效地表征限制的BV函数。作为应用程序，我们为$ {\ mathcal {\ widetilde {h}}_σ} $ - 限制的BV函数得出级别的定理。
For $a \ge - {( \frac{d}{2}- 1)^2} $ and $2σ= {d - 2}-( {{{(d - 2)}^2} + 4a})^{1/2}$, let $$\begin{cases}\mathcal{H}_{a}= - Δ+ \frac{a} {{{{ | x |}^2}}},\\ \mathcal{\widetilde{H}}_σ= 2\big( { - Δ+ \frac{σ^2} {{{{ | x |}^2}}}}\big)\end{cases}$$ be two Schrödinger operators with inverse-square potentials. In this paper, on the domain $Ω\subset {\mathbb {R}^d}\backslash \{ 0\}, d\geq 2,$ %apart from the origin, the ${\mathcal{H} _a}$-BV space $\mathcal{B} {\mathcal{V} _{{\mathcal{H} _a}}}(Ω)$ and the ${\mathcal{\widetilde{H}}_σ}$-BV space $\mathcal{B} {\mathcal{V} _{{\mathcal{\widetilde H} _σ}}}(Ω)$ related to $\mathcal{H}_{a}$ and $\mathcal{\widetilde{H}}_σ$ are introduced, respectively. We investigate a series of basic properties of $\mathcal{B} {\mathcal{V} _{{\mathcal{H} _a}}}(Ω)$ and $\mathcal{B} {\mathcal{V} _{{\mathcal{\widetilde H} _σ}}}(Ω)$. Furthermore, we prove that ${\mathcal{\widetilde{H}}_σ}$-restricted BV functions can be characterized equivalently via their subgraphs. As applications, we derive the rank-one theorem for ${\mathcal{\widetilde{H}}_σ}$-restricted BV functions.
