singular integral वाक्य
उदाहरण वाक्य
मोबाइल
- The " T " ( " b " ) theorem provides sufficient conditions for a singular integral operator to be a Calder�n & ndash; Zygmund operator, that is for a singular integral operator associated to a Calder�n & ndash; Zygmund kernel to be bounded on " L " 2.
- If " F " is a holomorphic univalent map from the unit disk " D " onto ? then the Bergman space of ? and its conjugate can be identified with that of " D " and " T " ? becomes the conjugate-linear singular integral operator with kernel
- Together they developed the ground-breaking theory of singular integral operators, thus creating the " Chicago School of ( hard ) Analysis " ( sometimes simply known as the " Calder�n-Zygmund School " ); this has been one of the most influential movements in pure mathematics, but with remarkable applications to science and engineering as well.
- From his methods on solving the Riemann problem had developed the theory of singular integral equations ( MSC ( 2000 ) 45-Exx ) which was entertained above all by the Russian school at the head of Nikoloz Muskhelishvili ( 8 : > ; 09 20 = > 28G CAE5; 8H28; 8 ) ( 1891 1976 ).
- This was accomplished by exploiting the interplay with probability and harmonic analysis, in the modern context ( the Central limit theorem, transference principles, square functions and other singular integral techniques are now part of the daily arsenal of people working in this area of ergodic theory ) and by attracting a number of talented mathematicians who have been very active in this area.
- The Calder�n-Zygmund memoir continues to be one of the most influential papers in the modern history of analysis; it laid the foundations of what became internationally known as the Calder�n-Zygmund School of Analysis ( or Calder�n-Zygmund decomposition lemma ", invented to prove the weak-type continuity of singular integrals of integrable functions, which is now widely used throughout analysis and probability theory.
- The most powerful, developed in the 1950s, provides global solutions of the equation on "'C "'and relies on the L " p " theory of the Beurling transform, a singular integral operator defined on L " P " ( "'C "') for all 1 " function from the closed disk to the closure of the domain.
- Among Krantz's research interests are : several complex variables, harmonic analysis, partial differential equations, differential geometry, interpolation of operators, Lie theory, smoothness of functions, convexity theory, the corona problem, the inner functions problem, Fourier analysis, singular integrals, Lusin area integrals, Lipschitz spaces, finite difference operators, Hardy spaces, functions of bounded mean oscillation, geometric measure theory, sets of positive reach, the implicit function theorem, approximation theory, real analytic functions, analysis on the Heisenberg group, complex function theory, and real analysis.
- By the mid 1960s the theory of singular integrals was firmly established by Calder�n's contributions to the theory of differential equations, including his proof of the " uniqueness in the Cauchy problem " using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary ( " the method of the Calder�n projector " ), and the crucial role played by algebras of singular integrals ( through the work of Calder�n s student R . Seeley ) in the " initial proof of the Atiyah-Singer Index Theorem ", see also the Commentary by Paul Malliavin . and Calder�n s proof of the " boundedness of the first commutator ".
- By the mid 1960s the theory of singular integrals was firmly established by Calder�n's contributions to the theory of differential equations, including his proof of the " uniqueness in the Cauchy problem " using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary ( " the method of the Calder�n projector " ), and the crucial role played by algebras of singular integrals ( through the work of Calder�n s student R . Seeley ) in the " initial proof of the Atiyah-Singer Index Theorem ", see also the Commentary by Paul Malliavin . and Calder�n s proof of the " boundedness of the first commutator ".
- By the mid 1960s the theory of singular integrals was firmly established by Calder�n's contributions to the theory of differential equations, including his proof of the " uniqueness in the Cauchy problem " using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary ( " the method of the Calder�n projector " ), and the crucial role played by algebras of singular integrals ( through the work of Calder�n s student R . Seeley ) in the " initial proof of the Atiyah-Singer Index Theorem ", see also the Commentary by Paul Malliavin . and Calder�n s proof of the " boundedness of the first commutator ".
- By the mid 1960s the theory of singular integrals was firmly established by Calder�n's contributions to the theory of differential equations, including his proof of the " uniqueness in the Cauchy problem " using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary ( " the method of the Calder�n projector " ), and the crucial role played by algebras of singular integrals ( through the work of Calder�n s student R . Seeley ) in the " initial proof of the Atiyah-Singer Index Theorem ", see also the Commentary by Paul Malliavin . and Calder�n s proof of the " boundedness of the first commutator ".
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