<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:77d9b4f3-1e9b-4350-83ea-b0254082bfc0,g:7375f414-00f3-4163-ad72-3e2221a33bd9-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:ck0001027596="http://usbank.com/20260626" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://usbank.com/20260626">
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/oef-rr/2025" schemaLocation="https://xbrl.sec.gov/oef/2025/oef-rr-2025.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001027596-20260626_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001027596-20260626_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001027596-20260626_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="ck0001027596_S000044707Member" abstract="true" name="S000044707Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_S000053713Member" abstract="true" name="S000053713Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_S000044708Member" abstract="true" name="S000044708Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_S000062254Member" abstract="true" name="S000062254Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_S000072390Member" abstract="true" name="S000072390Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000138961Member" abstract="true" name="C000138961Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000138962Member" abstract="true" name="C000138962Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_EconomicAndMarketRiskMember" abstract="true" name="EconomicAndMarketRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_ManagementRiskMember" abstract="true" name="ManagementRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_EquitySecuritiesRiskMember" abstract="true" name="EquitySecuritiesRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_ValueStyleInvestingRiskMember" abstract="true" name="ValueStyleInvestingRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MidCapCompanyRiskMember" abstract="true" name="MidCapCompanyRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_SectorEmphasisRiskMember" abstract="true" name="SectorEmphasisRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_LiquidityRiskMember" abstract="true" name="LiquidityRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_RealEstateInvestmentTrustREITRiskMember" abstract="true" name="RealEstateInvestmentTrustREITRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_DepositaryReceiptRiskMember" abstract="false" name="DepositaryReceiptRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_LimitedPartnershipAndMLPRiskMember" abstract="true" name="LimitedPartnershipAndMLPRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_ForeignSecuritiesRiskMember" abstract="true" name="ForeignSecuritiesRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_EmergingMarketsRiskMember" abstract="true" name="EmergingMarketsRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_CurrencyRiskMember" abstract="true" name="CurrencyRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_Russell1000TotalReturnReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" abstract="true" name="Russell1000TotalReturnReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_RussellMidcapRValueIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="RussellMidcapRValueIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000168873Member" abstract="true" name="C000168873Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000168874Member" abstract="true" name="C000168874Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_SmallCapCompanyRiskMember" abstract="true" name="SmallCapCompanyRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_Russell3000IndexReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" abstract="true" name="Russell3000IndexReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_Russell2000TotalReturnIndexReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" abstract="true" name="Russell2000TotalReturnIndexReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_Russell2000RValueIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="Russell2000RValueIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000138963Member" abstract="true" name="C000138963Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000138964Member" abstract="true" name="C000138964Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_FrontierMarketsRiskMember" abstract="true" name="FrontierMarketsRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_SectorEmphasisRiskFinancialServicesSectorRiskMember" abstract="true" name="SectorEmphasisRiskFinancialServicesSectorRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_RealEstateInvestmentTrustREITAndForeignRealEstateCompanyRiskMember" abstract="true" name="RealEstateInvestmentTrustREITAndForeignRealEstateCompanyRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIEmergingMarketsIndexNetUSDreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIEmergingMarketsIndexNetUSDreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIEmergingMarketsValueNetUSDreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIEmergingMarketsValueNetUSDreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000201595Member" abstract="true" name="C000201595Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000201596Member" abstract="true" name="C000201596Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_SectorEmphasisRiskIndustrialsSectorRiskMember" abstract="true" name="SectorEmphasisRiskIndustrialsSectorRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIWORLDExUSAIMIIndexNetUSDReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" abstract="true" name="MSCIWORLDExUSAIMIIndexNetUSDReflectsNoDeductionForFeesExpensesOrTaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIWORLDexUSASmallCapIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIWORLDexUSASmallCapIndexreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIWORLDexUSASmallCapValueIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIWORLDexUSASmallCapValueIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000228588Member" abstract="true" name="C000228588Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_C000228587Member" abstract="true" name="C000228587Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIEAFEIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIEAFEIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0001027596_MSCIEAFEValueIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" abstract="true" name="MSCIEAFEValueIndexNetreflectsnodeductionforfeesexpensesortaxesIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
</xs:schema>
