R. O. Hryniv

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Articles: 4

Self-adjointness of Schrödinger operators with singular potentials

Rostyslav O. Hryniv, Yaroslav V. Mykytyuk

↓ Abstract   |   Article (.pdf)

MFAT 18 (2012), no. 2, 152-159


We study one-dimensional Schrödinger operators $S$ with real-valued distributional potentials $q$ in $W^{-1}_{2,\mathrm{loc}}(\mathbb R)$ and prove an extension of the Povzner-Wienholtz theorem on self-adjointness of bounded below $S$ thus providing additional information on its domain. The results are further specified for $q\in W^{-1}_{2,\mathrm{unif}}(\mathbb R)$.

Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra

S. Albeverio, R. Hryniv, Ya. Mykytyuk

↓ Abstract   |   Article (.pdf)

MFAT 13 (2007), no. 2, 110-123


We study an inverse spectral problem for a compound oscillating system consisting of a singular string and $N$~masses joined by springs. The operator $A$ corresponding to this system acts in $L_2(0,1)\times C^N$ and is composed of a Sturm--Liouville operator in $L_2(0,1)$ with a distributional potential and a Jacobi matrix in~$C^N$ that are coupled in a special way. We solve the problem of reconstructing the system from three spectra---namely, from the spectrum of $A$ and the spectra of its decoupled parts. A complete description of possible spectra is given.

1-D Schrödinger operators with singular Gordon potentials

R. O. Hryniv, Ya. V. Mykytyuk

MFAT 8 (2002), no. 1, 36-48


1-D Schrödinger operators with periodic singular potentials

R. O. Hryniv, Ya. V. Mykytyuk

MFAT 7 (2001), no. 4, 31-42


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