• East Asian mathematical journal
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• v.40 no.5
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• pp.515-526
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• 2024

We consider the initial value problem of the Schrödinger equation for an Euler operator 𝓡 on ℂⁿ that is an analogue of the harmonic oscillator in ℝⁿ. We get some regularity results of the Schrödinger equation on Fock spaces.

• East Asian mathematical journal
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• v.35 no.1
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.