We prove essential self-adjointness for semi-bounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This is an extension of the Povzner–Wienholtz theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cu...

Spectra of the second derivative operators corresponding to the special PT -symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT -symmetric point interactions causing unusual spectral effects are investigated for the systems defined on a finite interval as well. The spectrum of this type of interactions is very far from the ...

Institutions were introduced by Goguen and Burstall [GB84, GB85, GB86, GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality bet...

We provide a shorter and more transparent proof of a result by I. Oleinik 25, 26, 27]. It gives a suucient condition of the essential self-adjointness of a Schrr odinger operator on a non-compact Riemannian manifold with a locally bounded potential in terms of the completeness of the dynamics for a related classical system. The simpliication of the proof given by I. Oleinik is achieved by an ex...

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point groups and the corresponding optimal subgroups are determined. Then, similarity reduction performed given equation some explicit solutions derived. asymptotic behaviours for also discussed. Through concept nonlinear self-adjointness...

We consider the quantum mechanics of a charged particle in presence Dirac’s magnetic monopole. Wave functions are sections complex line bundle and potential is connection on bundle. use continuum eigenfunction expansion to find an invariant domain essential self-adjointness for Hamiltonian. This leads proof Feynman–Kac formula expressing solutions imaginary time Schrödinger equation as stochast...

We discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators real principal type with null non-trapping condition, previously proved by Vasy (J Spectr Theory 10: 439–461, 2020) and Nakamura-Taira (Ann Henri Lebesgue 4: 1035–1059, 2021). For simplicity, here we second-order cases, i.e., Klein–Gordon-type only.