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The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Potential theory (Mathematics) --- Nonlinear theories --- Sobolev spaces --- Espaces de Sobolev --- Niet-lineaire theorieën --- Potentiaaltheorie --- Potentiel [Théorie du ] --- Ruimten van Sobolev --- Sobolev [Espaces de ] --- Sobolev [Ruimten van ] --- Spaces [Sobolev ] --- Theorieën [Niet-lineaire ] --- Théories non-linéaires --- Potential theory (Mathematics). --- Partial differential equations. --- Potential Theory. --- Partial Differential Equations. --- Partial differential equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics

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String models --- Superstring theories --- 530.19 --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Superstrings (Nuclear physics) --- Theories, Superstring --- Models, String --- String theory --- Nuclear reactions --- Elementary particles --- String models. --- Superstring theories. --- Modèles des cordes vibrantes (Physique nucléaire) --- Supercordes (Physique nucléaire)

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This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

Series, Infinite --- Analytic functions --- Harmonic analysis --- 515.243 --- Infinite series --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Mathematical Sciences --- General and Others --- Series, Infinite. --- Functions. --- Harmonic analysis. --- Differential equations --- Numbers, Complex --- Set theory --- Analytic functions. --- Functions

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To achieve their price stability objectives, many monetary authorities use the gap between current and potential output as an indicator of future price pressures. This policy-setting strategy has been criticized because potential output estimates have a high degree of uncertainty. In this paper, estimates of potential output uncertainty in New Zealand are used to examine the output gap’s usefulness. The results suggest that although output gap uncertainty leads to more inflation and output variability, policy based directly and/or indirectly on the output gap leads to better macroeconomic stability than policy based only on observable inflation and output growth.

Inflation --- Macroeconomics --- Money and Monetary Policy --- Production and Operations Management --- Monetary Policy --- Price Level --- Deflation --- General Aggregative Models: Forecasting and Simulation --- Macroeconomics: Production --- Prices, Business Fluctuations, and Cycles: General (includes Measurement and Data) --- Monetary economics --- Economic growth --- Output gap --- Potential output --- Inflation targeting --- Business cycles --- Production --- Prices --- Monetary policy --- Economic theory --- New Zealand

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This Selected Issues paper analyzes the background, stages and developments, and estimation of the direct costs of Paraguay's banking crisis. The paper provides the estimates on the size and evolution of the informal sector, and examines the extent to which the national accounts capture informal activity. The study also estimates the potential output and total factor productivity by examining trends in output, investment, and population growth as well as the direction and size of fiscal impulse on its economy. The paper also provides a statistical appendix report of Paraguay.

Banks and Banking --- Financial Risk Management --- Macroeconomics --- Public Finance --- Production and Operations Management --- Industries: Financial Services --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Fiscal Policy --- Macroeconomics: Production --- General Aggregative Models: General --- Production --- Cost --- Capital and Total Factor Productivity --- Capacity --- Financial Crises --- Banking --- Economic & financial crises & disasters --- Civil service & public sector --- Investment & securities --- Finance --- National accounts --- Fiscal stance --- Potential output --- Fiscal policy --- Loans --- Financial institutions --- Public sector --- Economic sectors --- Banks and banking --- National income --- Industrial productivity --- Economic theory --- Financial crises --- Paraguay