C*-ALGEBRA GENERATED BY INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS AND OSCILLATING COEFFICIENTS OF VARIOUS TYPES
نویسندگان
چکیده
We consider the C*-algebra, generated by multidimensional integral operators with homogeneous degree $$(-n)$$ kernels and of multiplication radial weak oscillating functions form $$|x|^{i\alpha }$$ . For this algebra, an operator symbolic calculus is constructed. In terms calculus, necessary sufficient conditions for Fredholm property are obtained.
منابع مشابه
Weighted Inequalities for Integral Operators with Some Homogeneous Kernels
In this paper we study integral operators of the form Tf(x) = |x − a1y| −α1 . . . |x − amy| mf(y) dy, α1 + . . . + αm = n. We obtain the L (w) boundedness for them, and a weighted (1, 1) inequality for weights w in Ap satisfying that there exists c > 1 such that w(aix) 6 cw(x) for a.e. x ∈ n , 1 6 i 6 m. Moreover, we prove ‖Tf‖BMO 6 c‖f‖∞ for a wide family of functions f ∈ L( ).
متن کاملOperators with C * - Algebra Generated by a Unilateral Shift
If T is an operator on a Hubert space %, this paper gives necessary and sufficient conditions on 7" such that C*(T), the C*-algebra generated by T, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which T is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C. R. Putnam as a consequence of o...
متن کاملexistence 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 ...
15 صفحه اولOn Integral Operators with Operator-Valued Kernels
It is well known that solutions of inhomogeneous differential and integral equations are represented by integral operators. To investigate the stability of solutions, we often use the continuity of corresponding integral operators in the studied function spaces. For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE’s, especially in the st...
متن کاملEigenvalue Decay of Integral Operators Generated by Power Series–like Kernels
We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either Rq or Cq . A power series-like kernel is a Mercer kernel having a series expansion based on an orthogonal family { fα}α∈Zq+ in L 2(X ,μ) , in which μ is a complete measure on X . As so, we show that the eigenvalues of the integral operators are given by an explicit formula d...
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: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05873-1