Geodesic
On a Certain Class of Commuting Systems of Linear Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 86-90

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In this paper we describe the class of commuting pairs of bounded linear operators $\{A_1,A_2\}$ acting on a Hilbert space $H$ which are unitarily equivalent to the system of integrations over independent variables $$ (\widetilde{A}_1f)(x,y)=i\int_x^af(t,y)\,dt,\qquad(\widetilde{A}_2f)(x,y)=i\int_y^bf(x,s)\,ds $$ in $L_{\Omega_L}^2$, where $\Omega_L$ is the compact set in $\mathbb{R}_+^2$ bounded by the lines $x=a$ and $y=b$ and by a decreasing smooth curve $L=\{(x,p(x)):p(x)\in C_{[0,a]}^1,\,p(0)=b,\,p(a)=0\}$.
Keywords: commutative system of linear non-self-adjoint operators, model approximation, operator with simple spectrum. 
V. A. Zolotarev. On a Certain Class of Commuting Systems of Linear Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 86-90. http://geodesic.mathdoc.fr/item/FAA_2012_46_4_a6/
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