Balayage of charge distributions and subharmonic functions onto a strip

We consider two balayage constructions on the complex plane $\mathbb{C}$ with real axis $\mathbb{R}$ for $0\le b\in \mathbb{R}$. Let $u\equiv ̸-\mathrm{\infty }$ be a subharmonic function on $\mathbb{C}$ of order $$\mathrm{ord}[u]:=\underset{z\to \mathrm{\infty }}{\mathrm{lim\hspace{0.17em}sup}}\frac{\ln \max \{1,u(z)\}}{\ln \mathrm{\mid }z\mathrm{\mid }}\le 1,$$ $U=u-v$ be the difference of subharmonic functions $u$ and $v\equiv ̸-\mathrm{\infty }$ on $\mathbb{C}$ with $\mathrm{ord}[v]\le 1$, i.e., $\delta$-subharmonic function on $\mathbb{C}$ of order $\mathrm{ord}[U]\le 1$. Then there is a $\delta$-subharmonic function $V\equiv ̸\pm \mathrm{\infty }$ on $\mathbb{C}$ of order $\mathrm{ord}[V]\le 1$ such that $V$ is harmonic on $\{z\in \mathbb{C}\mid \mathrm{\mid }\mathrm{\Re }z\mathrm{\mid }>b\}$ and $U(z)\equiv V(z)$ for all $z\in \bigl{ z \in \mathbb C\bigm| |\Re z|\leq b\bigr}\setminus E$where$E\subset \mathbb C$ is polar. If $u$ is a subharmonic function of finite type under order $1$, i.e., $$\underset{z\to \mathrm{\infty }}{\mathrm{lim\hspace{0.17em}sup}}\frac{u(z)}{\mathrm{\mid }z\mathrm{\mid }}<+\mathrm{\infty },$$ then there exist subharmonic functions $u_{\mathbb{R}}$ and $u_b$ of finite type under order $1$ that are harmonic respectively on $\mathbb{C}\setminus \mathbb{R}$ and $\bigl{ z \in \mathbb C\bigm| |\Re z|> b\bigr}$suchthat$$\begin{cases} u(z)\equiv u_{\mathbb R}(z)+u_b(z) \text{ for all $z\in {\mathbb R}\bigcup \bigl{ z \in \mathbb C\bigm| |\Re z|\leq b\bigr}$},\ u(z)\leq u_{\mathbb R}(z) + u_b(z) $\text{ for each }z\in \mathbb{C}\text{.}$\end{cases}$$ At the same time, we trace special relationships between the various logarithmic characteristics of the Riesz mass and charge distributions of subharmonic and $\delta$-subharmonic functions.