Relativistic integral equations with compact operator.—I.
نویسندگان
چکیده
منابع مشابه
Path Integral for Relativistic Equations of Motion
A c-number path integral representation is given for the solution of the KleinGordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic limit is briefly discussed from the point of view of the renormalization group.
متن کاملCompact Numerical Quadrature Formulas for Hypersingular Integrals and Integral Equations
In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals I [f ] = ∫ b a f (x) dx, where f (x)= g(x)|x − t |β , β being real. Depending on the value of β, these integrals are defined either in the regular sense or in the sense of Hadamard finite part. Assuming that g ∈ C∞[a, b], or g ∈ C∞(a, b) but can have arbitrary algebraic singularities at x ...
متن کاملCOLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS
In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of Fredholm-Volterra integral equations (FVIEs) are smooth.
متن کاملA Generalized Collectively Compact Operator Theory with an Application to Integral Equations on Unbounded Domains
In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to...
متن کاملIntegral Equations with Contrasting Kernels
0 C(t, s)x(s)ds with sharply contrasting kernels typified by C∗(t, s) = ln(e + (t − s)) and D∗(t, s) = [1 + (t − s)]. The kernel assigns a weight to x(s) and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for a ∈ L[0,∞), then solutions are largely indistinguishable regardless of which kernel is used. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Il Nuovo Cimento A
سال: 1969
ISSN: 0369-3546,1826-9869
DOI: 10.1007/bf02823306