zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Singular integral operators. Extended and partly modified translation from the German by Albrecht Böttcher and Reinhard Lehmann. (English) Zbl 0612.47024
Berlin etc.: Springer-Verlag. 528 p. DM 98.00 (Orig. Akademie-Verlag, Berlin) (1986).

The book is translated with some modifications from the German edition (1980; Zbl 0442.47027). It remains to indicate only the changes, incorporated by the translation.

In Chapter XI the new § 12 deals with the recent results on weighted norm inequalities for one-dimensional singular integral operators, due to R. Hunt. B. Muckenhoupt, R. Wheeden.

In Chapter XII the new § 7 is added, where polysingular integral operators with continuous coefficients are considered in the space L p ( 2 ) (results of I. Simonenko and V. Pilidi). In the same chapter § 8 deals with some basic notions for pseudo-differential operators in Sobolev-spaces W 2 (1) ( m ) (the boundedness, composition formula, parametrix,...).

In Chapter XVII, § 3 two new subsections (3.6 and 3.7) deal with the polynomial approximation method for singular integral equations over a finite interval with discontinuous coefficients. In the same chapter the new § 4 describes the spline collocation method for a one-dimensional singular integral equation.

In many other places new results can be found that have appeared within the 5 years after the first edition. References are extended on 150 new items.

Reviewer: R.Duduchava

MSC:
47B35Toeplitz operators, Hankel operators, Wiener-Hopf operators
47-02Research monographs (operator theory)
45E05Integral equations with kernels of Cauchy type
47GxxIntegral, integro-differential, and pseudodifferential operators
45P05Integral operators