we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltoni...

Abstract. We consider a periodic self-adjoint pseudo-differential operatorH = (−∆)m+ B, m > 0, in R which satisfies the following conditions: (i) the symbol of B is smooth in x, and (ii) the perturbation B has order less than 2m. Under these assumptions, we prove that the spectrum of H contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schrödinger operator...

We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this is result is a new Szegö formula for certain pseudo–differential operators. The formula j...

We propose a new consistent, residual-based stabilization of the Stokes problem. The stabilizing term involves a pseudo-differential operator, defined via a wavelet expansion of the test pressures. This yields control on the full L2-norm of the resulting approximate pressure independently of any discretization parameter. The method is particularly well suited for being applied within an adaptiv...

We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szegö formula for certain pseudo–differential operators. The formula just...

We give a program describing the pervasiveness of the short-time Fourier transform (STFT) in a host of topics including the following: waveform design and optimal ambiguity function behavior for radar and communications applications; vector-valued ambiguity function theory for multi-sensor environments; finite Gabor frames for deterministic compressive sensing and as a background for the HRT co...

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization A, we need a stability estimate for A as well. That condition is satisfied in particular, if A∗A is an elliptic pseudo-differential operator. We apply this scheme to show unique...

In this paper we construct and study a fundamental solution of Cauchy’s problem for p−adic parabolic equations of the type ∂u (x, t) ∂t + (f (D, β)u) (x, t) = 0, x ∈ Qnp , n ≥ 1, t ∈ (0, T ] , where f (D, β), β > 0, is an elliptic pseudo-differential operator. We also show that the fundamental solution is the transition density of a Markov process with state space Qp .