Murat Yurdakul

Remarks on strictly singular operators

A continuous linear operator

FT-IR, FT-Raman spectra, and DFT computations of the vibrational spectra and molecular geometry of chlorzoxazone.

T:E \to F

Molecular structure and vibrational spectra of 3-chloro-4-methyl aniline by density functional theory and ab initio Hartree-Fock calculations

is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon

HF and DFT studies of the structure and vibrational spectra of 8-hydroxyquinoline and its mercury(II) halide complexes

LB(E,F)=L_s(E,F)

Vibrational frequencies and structural determination of 2,2'-biquinoline

, which means that every continuous linear bounded operator defined on

Strictly singular operators and isomorphisms of Cartesian products of power series spaces

E

Restrictions of unbounded continuous linear operators on Fréchet spaces

into

HF and DFT studies and vibrational spectra of 1,2-bis(2-pyridyl)ethylene and its zinc (II) halide complexes

F

Isomorphic classification of Cartesian products of power series spaces.

is strictly singular.

Bounded operators and isomorphisms of Cartesian products of Fréchet spaces.

Far-IR, mid-IR, and FT-Raman spectra of the chlorzoxazone (CZX) were recorded. The observed vibrational wavenumbers were analyzed and assigned to different normal modes of vibration of the molecule. Density functional calculations were performed to support wavenumber assignments of the observed bands. The equilibrium geometry and harmonic wavenumbers of CZX were calculated by the DFT B3LYP method. All tautomeric forms and dimer form of CZX were determined and optimized. Additionally, experimental FT-IR spectrum in ethanol solution was recorded and compared with solid phase experimental data for the first time. The combination of the DFT B3LYP with polarized continuum model (PCM) was employed to characterize the solvent effects in ethanol solution.