Banach Bundles of Continuous Functions and an Integral Representation Theorem

INTEGRAL REPRESENTATION OF CONTINUOUS FUNCTIONS(x)

It was shown by F. Riesz [5; 350](2) that every subharmonic function u can be represented as the sum of the potential of its mass distribution plus a harmonic function; the potential appears in the form of a Stieltjes integral (Riesz's theorem is stated in (2.2.1)). We prove that the Stieltjes integral may be replaced by a Lebesgue integral if u is continuous, and if the lower generalized Lapla...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

An integral representation theorem of g-expectations

There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (1955), the other is the Peng’s g-expectation given by Peng (1997) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations u...

A Splitting Theorem for Holomorphic Banach Bundles

This paper is motivated by Grothendieck’s splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold X and a holomorphic Banach bundle E → X that is a compact perturbation of a trivial bundle in a sense recently introduced by Lempert. We prove that E splits into the sum of a finite rank bundle and a trivial bundle, provided H(X...

Integral Representation of Linear Continuous Operators from the Space of Lebesgue-bochner Summable Functions into Any Banach Space.