In this paper, we study the $$L^{1}$$ boundedness of Fourier integral operator $$T_{\phi ,a}$$ with rough symbol $$a\in L^{\infty }S^{m}_{\rho }$$ and a new class phase $$\phi $$ . class, extend $$L^{\infty }\Phi ^{2}$$ non-degeneracy conditions to some generalized derivative estimation measure condition respectively. Our main result substantially extends improves known results about operator. ...

This article constructs a surface whose Neumann-Poincar\'e (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The is sphere perturbed by smoothly attaching conical singularity, which imparts Rotational symmetry allows decomposition of the into Fourier components. Eigenvalues components are constructed so that they lie within spectrum other and thus full N...

In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H over the space J of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that par...

The asymptotic rates of convergence of thermodynamic properties with respect to the number of Fourier coeecients, k max , included in Fourier path integral calculations are derived. The convergence rates are developed both with and without partial averaging for operators diagonal in coordinate representation and for the energy. Properties in the primitive Fourier method are shown to converge as...

We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases. Concerning applications, several new results are obtained. From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we...

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...